The diameter of the base is the cone measured 8 units. The height measures 6 units.

What is the volume of the cone?

A) 24 π cubic units

B) 32 π cubic units

C)48 π cubic units

D)64 π cubic units

Answer:

m = [tex]\frac{2K}{v^2}[/tex]

Step-by-step explanation:

Given mass (m ) varies directly as K and inversely as v² then the equation relating them is

m = [tex]\frac{kK}{v^2}[/tex] ← k is the constant of variation

To find k use the condition m = 10 when K = 80 and v = 4 , then

10 = [tex]\frac{80k}{4^2}[/tex] = [tex]\frac{80k}{16}[/tex] ( multiply both sides by 16 to clear the fraction )

160 = 80k ( divide both sides by 80 )

2 = k

m = [tex]\frac{2K}{v^2}[/tex] ← equation of variation

The expression of mass as a function of kinetic energy and velocity is m = 2K/V².

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

We have been given that the mass varies directly as the Kinetic energy (K) and inversely as the square of the velocity (V).

m ∝ K/V²

m = cK/V²

Here c is the constant of variation,

If the kinetic energy is 80 Joules and the velocity is 4 meters per second, then the mass is 10 kilograms.

We have to determine the value of c

Here m = 10 , K = 80 and V = 4 , then

Substitute the values in m =  cK/V²

10 = c(80)/4²

10 = c(80)/16

10 = 5c

c = 10/5

c = 2

Substitute the value of c = 2 in the equation of variation,

⇒ m = 2K/V²

Hence, the expression of mass as a function of kinetic energy and velocity is m = 2K/V².

Learn more about the expressions here:

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The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.

Recall :

Evaluating an hypothetical scenario :

Let standard deviation, σ = 2

Sample size = 50

Margin of Error = 2/√50 = 0.554

Using Quadruple of the sample size : (50 × 4) = 200 samples

(0.227 ÷ 0.554) = 0.5

Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.

Learn more : https://brainly.com/question/13403969

Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.

799 x 0.70 = 559.30

549 x 0.70 = 384.30

Total: 559.30 + 384.30 = $943.60

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

Answer:

[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]

Step-by-step explanation:

Given

[tex](4x^3y^5)(3x^5y)^2[/tex]

Required

The equivalent expression

We have:

[tex](4x^3y^5)(3x^5y)^2[/tex]

Expand

[tex](4x^3y^5)(3x^5y)^2 = 4x^3y^5*9x^{10}y^2[/tex]

Further expand

[tex](4x^3y^5)(3x^5y)^2 = 4*9*x^3*x^{10}y^5*y^2[/tex]

Apply laws of indices

[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

Answer:

Step-by-step explanation: Hello! Do

Step-by-step explanation:

f(x)=log(x)

     =d(log(x)/dx)

=>y=1/x

Step-by-step explanation:

the answer is regular octagon

i think

Answer:

A∩B ={2;4}

Step-by-step explanation:

Chúc bạn học tốt

Answer:

It's option D. y = 1/2x - 4

Step-by-step explanation:

I used Desmos to find the answer, hope the graph helps!

C 89. What is the power of 5, so that 1 its value become ?

The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.

Answer:

74.80

Step-by-step explanation:

First find the discount

88 * 15%

88*.15

13.2

Subtract the discount from the original price

88-13.2

74.80

The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: [tex]10.5k= 3214[/tex]

The page dimension is:

[tex]Length = 12[/tex]

[tex]Width = 12[/tex]

The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square

The margin of 0.75 on either sided means the usable dimension is:

[tex]Length = 12 - 2 * 0.75 =10.5[/tex]

The dimension of India is:

[tex]Length = 3214[/tex]

[tex]Width =2933[/tex]

The longest side in India's dimension is:

[tex]Longest = 3214[/tex]

From Uche's book, the longest dimension is:

[tex]Longest = 10.5[/tex]

So, the scale equation is:

k * longest length of Uche's book = longest side of India

This gives:

[tex]k * 10.5 =3214[/tex]

[tex]10.5k =3214[/tex]

Read more about scale ratio at:

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9514 1404 393

Answer:

  C. none of these

Step-by-step explanation:

The given information tells us ΔACD is isosceles, but gives no information about any lines that might conceivably be parallel.

Answer:

what's is the question anyway

Answer: 20 ft³

Step-by-step explanation:

volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]

Therefore, the volume is:

[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]

Answer:

f(- 10) = 150

Step-by-step explanation:

f(- 10) with t = - 10 corresponds to t ≤ - 10 with f(t) = t² - 5t , then

f(- 10) = (- 10)² - 5(- 10) = 100 + 50 = 150

for t=-10

So

f(-10)

Step-by-step explanation:

I am not sure but is this question like this

if it's not i am sorry

Answer:

no

Step-by-step explanation:

-7+x^2-3x      =       9+x-10

-7+(-2)^2-3*(-2)                   9+(-2)-10

-7+4+6                                9-12

3                   >                      -3

if we substitute -2 to x, answer is not equal

Answer:

x= -2

-7 +x^2 - 3x = 9 +x - 10

-7 + (-2)^2 -3×(-2) = 9 + (-2) -10

-7 +4 +6 = 9 - 2 - 10

-7+10=9-12

3 =-3

Don't blame me if this is incorrect:)

Answer:

Option b: Rectangle

Explanation:

Give branliest pls ;)

Answer:

21/8 yds or 2 5/8 yds

Step-by-step explanation:

First turn 1 3/4 yards into an improper fraction so you can add it to 7/8 yards.

1 3/4 as an improper fraction is 7/4 yds

7/4 yds = 14/8 yds

14/8 yds + 7/8 yds = 21/8 yds

So the total amount of ribbon Amanda has is 21/8  yds or 2 5/8 yds

Answer:

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

150 guests booked:

This means that [tex]n = 150[/tex]

85% of booked guests show up for their room.

This means that [tex]p = 0.85[/tex]

Is the normal approximation suitable:

[tex]np = 150(0.85) = 127.5[/tex]

[tex]n(1-p) = 150(0.15) = 22.5[/tex]

Both greater than 10, so yes.

Mean and standard deviation:

[tex]\mu = E(X) = np = 150*0.85 = 127.5[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732[/tex]

Find the probability that if the motel books 150 guests, not enough seats will be available.

More than 140 show up, which, using continuity correction, is [tex]P(X > 140 + 0.5) = P(X > 140.5)[/tex], which is 1 subtracted by the p-value of Z when X = 140.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140.5 - 127.5}{4.3732}[/tex]

[tex]Z = 2.97[/tex]

[tex]Z = 2.97[/tex] has a p-value of 0.9985.

1 - 0.9985 = 0.0015.

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Answer:

x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4

Step-by-step explanation:

Using quadratic formula, x=(-1±sqrt(1-48))/4.

x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4

Answer:

If you do not understand any steps, please feel free to comment down below.

Answer:

breathing, jk buddy

Step-by-step explanation:

9514 1404 393

Answer:

  9 square inches

Step-by-step explanation:

The area is proportional to the square of the linear scale factor. We can use this to write the proportion ...

  A/(144 m²) = ((2 in)/(8 m))²

  A = (144·4/64) in² = 9 in²

The area representing 144 square meters is 9 square inches.

===========================================================

Explanation:

The given function is

[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}[/tex]

which is the same as writing f(x) = ( sqrt(2x-6) )/(x-3)

The key for now is the square root term. Specifically, the stuff underneath. This stuff is called the radicand.

Recall that the radicand cannot be negative, or else the square root stuff will result in a complex number. Eg: [tex]\sqrt{-4} = 0+2i[/tex]

The question is basically asking: what is the smallest x such that [tex]\sqrt{2x-6}[/tex] is a real number?

Well if we made 2x-6 as small as possible, ie set it equal to 0, then we can find the answer

[tex]2x-6 = 0\\\\2x = 6\\\\x = 6/2\\\\x = 3\\\\[/tex]

I set the radicand equal to 0 because that's as small as the radicand can get (otherwise, we're dipping into negative territory).

So 2x-6 set equal to 0 leads to x = 3.

This means x = 3 produces the smallest radicand (zero) and therefore, it is the smallest allowed x value for that square root term.

But wait, if we tried x = 3 in f(x), then we get...

[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}\\\\f(3) = \frac{\sqrt{2*3-6}}{3-3}\\\\f(3) = \frac{\sqrt{0}}{0}\\\\[/tex]

which isn't good. We cannot have 0 in the denominator. Dividing by zero is not allowed. The result is undefined. It doesn't even lead to a complex number. So we'll need to bump x = 3 up to x = 4. You should find that x = 4 doesn't make the denominator 0.

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

In short, we found that x = 3 makes the square root as small as possible while staying a real number, but it causes a division by zero error with f(x) overall. So we bump up to x = 4 instead.

Answer:

no entiendo inglés........,

Hi,

Answer:

Tachycardia is a fast heart rate

Answer:

2nd option, rectangle B

Step-by-step explanation:

After reflexion, the figure will be at the left side of x=-5

Part (a)

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

Explanation:

L = 2.4 = length

W = unknown width

The perimeter of any rectangle is P = 2(L+W)

We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2

========================================================

Part (b)

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

Explanation:

We'll solve the equation we set up in part (a)

2(2.4+w) = 14.2

2(2.4)+2(w) = 14.2

4.8+2w = 14.2

2w = 14.2-4.8

2w = 9.4

w = 9.4/2

w = 4.7

The width must be 4.7 cm.