n the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside. A cone is inside of a pyramid with a square base. The cone has a height of h and a radius r. The pyramid has a base edge length of 2 r. Which statement best describes where the StartFraction pi Over 4 EndFraction comes from in the formula derivation? It is the ratio of the area of the square to the area of the circle from a cross section. It is the ratio of the area of the circle to the area of the square from a cross section. It is the difference of the area of the square and the area of the circle from a cross section. It is the sum of the area of the square and the area of the circle from a cross section.

Total cards left

Total hearts left

Probability

Option B

Answer:

[tex]\sf F. \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

A deck of 52 playing cards contains 13 hearts.

If Sara has 12 cards from this deck in her hand and 3 of them are hearts, then:

Total cards remaining in the deck

= total deck - cards Sara has

= 52 - 12

= 40

Total hearts left in the remaining deck

= total heart cards - heart cards Sara has

= 13 - 3

= 10

So there are 40 cards in the deck and 10 of them are hearts.

Probability Formula[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore, the probability that a card drawn at random from the remainder of the deck will be a heart is:

[tex]\begin{aligned}\implies \sf P(heart) & =\dfrac{\textsf{number of hearts in remaining deck}}{\textsf{total cards in remaining deck}}\\\\ & =\dfrac{10}{40}\\ \\& =\dfrac{1}{4}\end{aligned}[/tex]

Answer:

g(x)=-32x

Step-by-step explanation:

When something is reflected over the x-axis. The x doesn't change, it's the y that changes. So let's just generally say you have the point (x, y). Reflecting this over the x-axis means the y is changing, so it becomes (x, -y). And since the g(x) represents the y, you multiply the entire thing by -1. So the new equation becomes: g(x) = -(8(4x)) = -8(4x) = -32x. So the equation is g(x) = -32x or -8(4x) if you want to leave it like how it was before.

Hence, the inverse of the given function is [tex]{(\frac{x}{10})}^5 - 2[/tex]

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.

given function,

                 q(x) = 10[tex]\sqrt[5]{x-2}[/tex]

say y=q(x)

now we have,

                y = 10[tex]\sqrt[5]{x-2}[/tex]

                [tex]\frac{y}{10}[/tex] = [tex]\sqrt[5]{x-2}[/tex]

raising to 5th power on both sides,

               [tex](\frac{y}{10})^5[/tex] = x - 2

               x =  [tex](\frac{y}{10})^5[/tex] + 2

               [tex]q^{-1}(x) =[/tex] [tex]{(\frac{x}{10})}^5 - 2[/tex]

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The correct option based on the paralel line given is that the corresponding angles are congruent.

Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.

We are to find the reason for the second step in the following proof. Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3

Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.

And, therefore we get ∠1 ≅ ∠2.

Thus, the reason in the second step will be angles 1 and 3 are corresponding angles and corresponding angles are congruent.

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Using proportions, the value of x is given as follows: x = 16

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We are given this following proportion:

[tex]\frac{n}{4} = \frac{k}{x}[/tex]

In this problem, we have that n = 15 and k = 60, hence:

[tex]\frac{15}{4} = \frac{60}{x}[/tex]

Applying cross multiplication:

15x = 60 x 4

Simplifying by 15:

x = 4 x 4

x = 16.

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Answer:

A. (2,3)

It is rather simple the 9 points between a and B 2/3 of that is 6

Among all the given equations 6(x+3)+x=7x+9+9 is having many solutions.

Given Equations :

6(x+3)+x=7x+2+1

6(x+3)+3=7x+5

6(x+3)+x=6x+3+15

6(x+3)+x=7x+9+9

We have to find the equation having many solutions.

The equation whose both sides are equal to each other is supposed to have many solutions. For determining all equations needs to be solved.

Equation 1

6(x+3)+x=7x+2+1

6x+18=7x+3

No the above equation is not having many solutions.

Equation 2

6(x+3)+3=7x+5

6x+18+3=7x+5

6x+21=7x+5

No the above equation is not having many solutions.

Equation 3

6(x+3)+x=6x+3+15

6x+18+x=6x+18

7x+18=6x+18

No the above equation is not having many solutions.

Equation 4

6(x+3)+x=7x+9+9

6x+18+x=7x+18

7x+18=7x+18

Yes the above equation is having many solutions.

Hence the equation which is having many solutions is 6(x+3)+x=7x+9+9.

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The options given in the question are wrong and the correct options are as under:

1) 6(x+3)+x=7x+2+1

2)6(x+3)+x=7x+5

3)6(x+3)+x=6x+3+15

4) 6(x+3)+x=7x+9+9

Answer:

y=-0.012x(x-200).

Step-by-step explanation:

1) the given parabola has two zeros: 0 and 200. It means, the required equation is: y=ax(x-200), where a - unknown number;

2) according to the given graph the vertex is (100; 120). It is possible to substitute the coordinates of it into the equation y=ax(x-200) and calculate the value of 'a':

120=a*100(100-200); ⇒ a=-0.012.

3) finally, the required equation is:

[tex]y=-0.012x(x-200).[/tex]

the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:

36*36 = 1,296

Now if we define the outcomes as:

{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }

The outcomes that give at most a sum of 8 are:

{1, 1, 1, 1}

{2, 1, 1, 1} ( 3 permutations)

{2, 2, 1, 1} ( 6 permutations).

{2, 2, 2, 1} ( 3 permutations)

{3, 1, 1, 1} ( 3 permutations)

{3, 2, 1, 1} ( 12 permutations)

{3, 3, 1, 1} (6 permutations)

{4, 1, 1, 1} (3 permutations)

{4, 2, 1, 1} (6 permutations)

{5, 1, 1 , 1} (3 permutations)

{2, 2, 2, 2}

These are all the outcomes that give a sum of, at most, 8.

If we add all the outcomes we get 47 outcomes.

Then the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

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The product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x

The expression is given as:

(a^2x^3 -5x+3a).(-2a^3x)

Open the bracket

-2a^3x * a^2x^3 -2a^3x * - 5x -2a^3x * 3a

Evaluate the products

-2a^5x^4 + 10a^3x^2 - 6a^4x

Hence, the product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x

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By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

Trigonometric Identities exist as the equivalencies that apply trigonometry operations and have true for all the values of variables shown in the equation. There exist different trigonometric identities concerning the side length as nicely as the angle of a triangle.

How to simplify the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]?

Given:

[tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

General solution for [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

then from the general equation, we get

[tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] and

[tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] then [tex]$x= -2n\pi +\frac{\pi}{3}[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]then [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Therefore, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Radians, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Degree, [tex]$x = 60 \degrees- 360\degree n[/tex], [tex]$x = -60\degree- 360\degree n[/tex]

By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

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Answer:

             x     +             6      ≥        15

Step-by-step explanation:

Add any number greater than equal to 9 to the number 6 and you get a result of at least 12. Any number less than 9 produces a result that is not at least 15.

Just saying the question was not that descriptive so I don't know if this is what you asked for... Sorry!

(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].

(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].

So, the combined areas of the four semicircles is [tex]241\pi[/tex].

The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].

Answer:

.

Step-by-step explanation:

A parallelogram has two pairs of parallel lines so if AD // BC and that AD//BC, Then it is indeed a parallelogram

Final answer:

The difference of the elevations is 30347 feet.

Step-by-step explanation:

Step 1

The highest elevation is 29028 feet.

Step 2

The lowest elevation is -1319 because it is below the sea level.

Step 3

The difference of the elevations is:

29028 - (-1319)

Step 4

Evaluate the value of expression:

29028 - (-1319) = 30347

Answer:

Hope it helps!!

Answer:

[tex]a < 0[/tex]   False

[tex]|a| > 0[/tex] True

[tex]|a|=0[/tex]  False

________________________________________________

a is on the right side of 0,

which means a is positive.

The absolute value is the distance to zero (always positive)

Which means the absolute value of a is also positive.

[tex]a < 0[/tex]   is wrong because a is positive

[tex]|a| > 0[/tex]  is correct because a is larger than 0

[tex]|a|=0[/tex]  is wrong because [tex]a[/tex] ≠ [tex]0[/tex]

________________________________________________

Hope this helps :)

The expression which equals 24 is (4 + 2) (3) . Option B

Given the following expression

Let's evaluate each of them. we have

(2 + 4)(3) = 6× 3 = 18

(4 x 2)(3) = 8 × 3 = 24

(4 - 2) + 3 (4 + 3) - 2 = 2 + 3(7) -2 = 2 + 21 - 2 = 23 -2 = 21

Thus, the expression which equals 24 is (4 + 2) (3) . Option B

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Answer:

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.

The thing that's wrong with the equation is that 2 shouldn't be multiplied by 4 but should have been added.

From the information given, it can be seen that the equation is:

(3x²)(-2x⁴) = 3(-2)x² × x⁴ = 6x^8

Based on the information above, this calculation is incorrect. The correct calculation will be:

(3x²)(-2x⁴) = 3(-2)x² × x⁴

= -6x^6

Therefore, the multiplication should be an addition of the power.

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Answer:

B i think

Step-by-step explanation:

The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5 and the frequency of the most frequent number of over-the-limit items is 14

The most frequent number of over-the-limit items for this data set is the dataset that has the highest frequency.

This is represented by the class that has the highest bar on the histogram

To do this, we simply check the class that has the highest bar on the histogram.

From the attached histogram the class that has the highest bar on the histogram is 3.5 - 4.5

Hence, the most frequent number of over-the-limit items for this dataset is 3.5 - 4.5

In (a), we have:

The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5

Next, we check the frequency of the most frequent number of over-the-limit items for this dataset

According to the histogram, the most frequent number of over-the-limit items for this dataset has a frequency of 14

Hence, the frequency of the most frequent number of over-the-limit items is 14

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Answer:

200

Step-by-step explanation:

it was found that the ratio of people who liked Arithmetic and Algebra is 9 : 8. If 25% liked the both, 80 liked none of these and 20% liked arithmetic only, find the total number of people participated in the survey. Ans: 200

If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.

Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.

Amount from store forms an equation.

let the amount earned from college is x.

According to question:

Amount earned from store=4x+1250

Amount earned from college=x

Total amount earned=4x+1250+x

5x+1250=15450

5x=15450-1250

5x=14200

x=14200/5

x=2840

Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.

Hence the amount earned by Erica from college is $2840.

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The system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

From the question, we are to determine the system of inequalities that represents the graph

The equation of the solid line is  y = -x +4

Since the lower part of the graph was shaded

Then,

The inequality that represents the solid line is

y ≤ -x +4

The equation of the dotted line is  y = 3x -1

Since the lower part of the graph was shaded,

Then,

The inequality that represents the solid line is

y < 3x-1

Hence, the system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

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Answer:

B ∩ (A ∪ C)'

Step-by-step explanation:

It's the B part excluding A and C union. Hence,

(A ∪ C)' ∩ B

Answer:

First one

Step-by-step explanation:

First one ....pick a point ....say C    for 'x'   add 8    for y   subtract 3  and you will be at C'

Answer:

A. Coffee 4C below the freezing point

Step-by-step explanation:

Negative temperature when talking about water means below the freezing point (below 0). Look up number line. Negative 4 is below 0 whereas positive 4 is above 0. Thus, option A is the best answer

Answer:

A

Step-by-step explanation:

This is because negative number start below zero and since water freezes at zero degrees celsius, Mia's iced coffee is below the freezing point.

There are two interpretations we could go for:

Check out the diagram below.

Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.

Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.

The equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

The given coordinates are (3,0) and (4,4).

The formula to find the slope of an equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

Now, slope[tex]=\frac{4-0}{4-3} =4[/tex].

The equation of the line is [tex](y-y_{1} )=m(x-x_{1} )[/tex]

⇒(y-3)=4(x-0)

⇒y-3=4x

⇒4x-y+3=0

Therefore, the equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

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