Simplify the following expression.


A.

B.

C.

D.

Answer:

Cone: h =  [tex]3\frac{V}{\pi r^{2} }[/tex]

Cylinder: h = [tex]\frac{V}{\pi r^{2} }[/tex]

Step-by-step explanation:

- the formula you described is not the formula for the volume of a cone as it is V = [tex]\pi rx^{2} \frac{h}{3}[/tex]

- to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:

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

- based on the formula you described, it is closer to a cylinder and the formula for the volume of a cylinder is: V = [tex]\pi r^{2} h[/tex]

- once again, to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:

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

hope this helps :)

Answer:

(a) 50:

3 53 103

(b) 60:

7 67 127

11 71 131

Step-by-step explanation:

OK, I think you can prove this with the theorem that any prime greater than 3 is 6n-1 or 6n+1, for integer n. In other words, any prime is near a multiple of 6; it is either one less or one more. The proof for this is very easy, look it up.

Given this fact, if two primes (p,q) are 70 a part, this means the first one has to be a case of 6n+1 and the second one has to be a case of 6n-1. Why? Because the nearest multiple of 6 is 72 and with +1 on one end and -1 on the other end, you can reach a "gap" of 70.

Now for the next two primes (q,r) the same must hold. Only, it can't because this requires q to be both 6n-1 and 6n+1.

Answer:

y=mx+b is the formula starting with b say it is 4 you put a dot on 4  on the y axis m is 1/2 you go up 1 right 2 on the 4 points then do the same on the next point you get then you get your line. hope this helps  

Answer:

55.5

Step-by-step explanation:

answer is 55.491477012331599 which rounded to the nearest tenth is 55.5

when you said to the nearest tenth of degree i assume that meant like rounding to the nearest tenth

The transformation of the function, y=1/7 x from y = x is y = 7x

The function is given as:

y = 1/7x

The transformation rule is given as:

y = x

This means that we swap x and y.

So, we have:

x = 1/7 y

Multiply through by 7

y = 7x

Hence, the transformation of the function, y=1/7 x from y = x is y = 7x

Read more about transformation at:

https://brainly.com/question/5994940

#SPJ1

Here is the frequency table:
Class       Frequency

15 - 24       4

25 - 34        9

35 - 44       2

45 - 54        7

55 - 64         7

65 - 74          1

A frequency table is used to track the frequency of a data set. The data ranges from 15 to 68, if the classes are to be 6, then the class interval would have to be 9.

Class       Frequency

15 - 24       4

25 - 34        9

35 - 44       2

45 - 54        7

55 - 64         7

65 - 74          1

To learn more about frequency tables, please check: https://brainly.com/question/12576014

#SPJ1

The area that the plane can fly and be in the zone known as the Bermuda is; 346952 mile²

The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.

Now, from the question, we are give;

Side 1 = 900 miles

Side 2 = 930 miles

Angle between two sides = 56°.

Thus, by the area rule we have;

Area = (1/2) * 900 * 930 * sin 56°

Area = 346952 mile²

Read more about Area rule at; https://brainly.com/question/20839703

#SPJ1

You should write down and track only the 20lbs weight during your weighted exercise while ignoring your body weight.

Actual weight is also referred to as gross weight and it can be defined as the exact (original) weight of an object, as measured using an appropriate weighing scale.

This ultimately implies that, you would write down and track only the 20lbs weight during your weighted exercise such as a single rep of weighted overhand chin ups.

Read more on actual weight here: https://brainly.com/question/2335828

#SPJ1

The probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.

The Poisson distribution is a discrete probability distribution that describes the likelihood of a specific number of events occurring in a specified span of time or space, if these events occur at a constant mean rate and regardless of the time since the last occurrence.

Let X ~ Pois(λ)

Then we have:

E(X) = λ = Var(X)

Since standard deviation is the square root (positive) of variance,

Thus,

The standard deviation of X = [tex]\sqrt{\lambda}[/tex]

Its probability function is given by

[tex]f(k; λ) = Pr(X = k) = \dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]

Given the mean is 4.2.

We have to find the probability that on any day, the number of special orders sent out will be exactly 3. Therefore, the value of x will be 5.

Using the Poisson distribution,

[tex]P(x) = \dfrac{e^{-\lambda}\lambda ^x}{x!}\\\\P(5) =\dfrac{e^{-4.2}(4.2)^5}{5!}\\\\P(5) = 0.1633[/tex]

Hence, the probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.

Learn more about Poisson distribution here:

https://brainly.com/question/7879375

#SPJ1

Answer: [tex]8x^6 y^3[/tex]

Step-by-step explanation:

See attached image.

The expression which is equivalent to (2x²y)³ is 8x⁶y³

An expression is combination of variables, numbers and operators.

The given expression is (2x²y)³

Two times of x square times of y whole to the power of three

We have to find the equivalent expression of the given expression.

Equivalent expressions are expressions that work the same even though they look different.

We have a property that [tex](a^m)^n=a^m^n[/tex]

So (2x²y)³ = 2³x⁶y³

=8x⁶y³

Hence, the expression which is equivalent to (2x²y)³ is 8x⁶y³

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ5

Answer:

It does not.

Step-by-step explanation:

[tex]6(2x - 6) = -7(-2x + 4); \\ 6 * 2x - 6 * 6 = -7 * (-2x) + (-7) * 4; \\ 12x - 36 = 14x - 28; \\ 14x - 12x = -36 + 28; \\ 2x = -8; \\ x = -4.[/tex]

[tex]\{-4\}[/tex] is our set of solutions. Answering your question, it does not.

Answer:

so from my opinion Robert give them a Smack in their ases .

Hope this helps .

Good luck ✅.

Answer:

50.3cm²

Step-by-step explanation:

Formula: The area of a circle is found by A = πr²

Given:

Plug in:

A = πr² → A = (3.142)(4)²

            → A = (3.142)(16)

            → A = 50.272

"1 decimal places",  round up to 50.3

Learn more about Circles here: https://brainly.com/question/10368742

The value of k in g(x) = 5^x + k is -7

The complete question is added as attachment

The functions are given as:

f(x) = 5^x

g(x) = 5^x + k

From the attached graph, we can see that:

f(x) is shifted down by 7 units to form g(x)

This means that:

g(x)= f(x) - 7

This gives

g(x) = 5^x - 7

Substitute g(x) = 5^x - 7 in g(x) = 5^x + k

5^x + k = 5^x - 7

This gives

k = -7

Hence, the value of k in -7

Read more about translation at:

https://brainly.com/question/12802998

#SPJ1

The critical value of r is mathematically given as r = +0.487, with no significant linear correlation. Option A.

Question Parameters

r = -0.868

n = 5

df = 5 - 2

df = 3

[tex]\alpha / 2 =0.025[/tex]

Critical values [tex]r= \pm 0.878[/tex]

Generally, there exists no linear correlation between the Critical values

as r=0.878

In conclusion,  Critical values: r = +0.487, no significant linear correlation

Read more about Critical values

https://brainly.com/question/14508634

#SPJ1

Answer:

[tex]\displaystyle g(x) = -(x + 2)(x - 4)[/tex]

Step-by-step explanation:

First, look at the graph to determine whether it opens down or up, which in this case is down, so you insert a negative in front of the expression. Next, locate your x-intercepts [zeros (where the graph insects the x-axis)]. You will see that the graph intersects [tex]\displaystyle [-2, 0][/tex] and [tex]\displaystyle [4, 0],[/tex] so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation, [tex]\displaystyle y = A[x - h]^2 + k,[/tex] that negative in front of [tex]\displaystyle h[/tex] gives you the OPPOCITE outcome, so be careful.

I am joyous to assist you at any time.

The coefficients of variation shows that D. The grade point averages of females are more variable than males.

From the complete information, the coefficients of variation for male is 21.3% and the coefficient of variation for female is 25.1%.

In this case, the coefficients of variation shows that the grade point averages of females are more variable than males.

In conclusion, the correct option is D.

Learn more about coefficient of variation on:

brainly.com/question/19616808

#SPJ1

Answer:

It would be B.

Step-by-step explanation:

[tex]area = l \times w \\ but \: w = l - 2[/tex]

[tex]area = l(l - 2) = l {}^{2} - 2l[/tex]

[tex]l {}^{2} - 2l \geqslant 48 \\ l {}^{2} - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0[/tex]

[tex]l {}^{2} - 2l \leqslant 80 \\ l {}^{2} - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0[/tex]

Answer:

[tex]1200\times6.75=R8100[/tex]

The missing value of the ordered triple for questions 7,8,9 and 10 will be  y=2,x=6,z=0, and z=-5 respectively.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The given equation in the problem is;

7) (4, ,0)

Substitute the values in the equation;

⇒x+2y-3z = 8,

⇒4+2y-3(0) = 8

⇒2y=8-4

⇒2y=4,

⇒y=4/2

⇒y=2

8) (, -2, -2)

Substitute the values in the equation;

x+2(-2) -3(-2)= 8

x-4+6 =8

x= 8-6+4

x=8-6+4

x=6

9)(2, 3, )

Substitute the values in the equation;

⇒2+2(3)-3z = 8

⇒8-3z = 8

⇒-3z = 0

⇒z = 0/-3

⇒z= 0

10) (-3, -2, )

Substitute the values in the equation;

⇒-3+2(-2) -3z = 8

⇒-7 -3z = 8

⇒-3z = 15

⇒z = 15/-3

⇒z = -5

Hence, the missing value of the ordered triple for questions  7,8,9, and 10 will be  y=2,x=6,z=0, and z=-5 respectively.

To learn more, about equations, refer;

https://brainly.com/question/10413253

#SPJ1

A pair of the opposite sides of a hexagon has equal length and this is proved below.

It should be noted that a hexagon is a polygon that has six sides.

In this case, it has 6 sides.

The total angles will be:

= (n - 2) × 180

= (6 - 2) × 180

= 720°

Each angle will hence be:

= 720°/6

= 120°

Each angle are equal and this illustrates that the parallel sides are equal.

A diagram is attached to illustrate the pair of parallel sides.

Learn more about hexagon on:

brainly.com/question/1615720

#SPJ1

Answer:

300

Step-by-step explanation:

A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula: 

Volume= 1/3 × Base area × Height

The equation of the transformed function is y = 1/2(x - 4)^3 + 5

The parent function is given as:

y = x^3

When the function is vertically compressed by 1/2, the rule is:

(x, y) ⇒ (x, 1/2y)

So, we have

y = 1/2x^3

When translated 4 units right, we have:

y = 1/2(x - 4)^3

When translated 5 units up, we have:

y = 1/2(x - 4)^3 + 5

Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5

Read more about function transformation at:

https://brainly.com/question/3381225

#SPJ1

The number of students who voted is 240.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

The number of students who voted = number of votes Sari received / percentage number

60 / 0.25 = 240

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

Answer:

134,784 people

Step-by-step explanation:

Hello!

Let's first find the number of people it can carry on 1 trip. We can do this by multiplying the number of people per coach, by the number of coaches.

The train carries 864 people per trip. We can find the number of people in 156 trips by multiplying 864 by 156.

The train, in full capacity, will carry 134,784 people in 156 trips.

Dividing both sides by rt,

[tex]\boxed{P=\frac{I}{rt}}[/tex]

Using the conversion from the 24-hour system to the AM/PM system, the patient should take the medicine at 10 PM.

22 divided by 12 has remainder 10, hence 22 is equivalent to 10 PM.

More can be learned about the conversion from the 24-hour system to the AM/PM system at https://brainly.com/question/17477625

#SPJ1

The mixed number equivalent to the fraction 28 / 5 is 5 3 / 5

A fraction represented with its quotient and remainder is a mixed fraction.

Therefore, it is a combination of a whole number and a proper fraction.

Hence,

The fraction is in improper fraction, let's convert it to mixed fraction.

Therefore,

28 / 5 = 5 3 / 5

learn more on fraction here: https://brainly.com/question/11709591

#SPJ1

Answer:

Could you please provide more context to the problem

Step-by-step explanation:

There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.