find the limit. (if the limit is infinite, enter '[infinity]' or '-[infinity]', as appropriate. if the limit does not otherwise exist, enter dne.) lim x→[infinity] 16x2 x − 4x

The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

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Answer:

Step-by-step explanation:

Let the distance be x

Then Jonathan biked for

His mother drew for

The time difference is

So we have

Answer:

I think option (D) 4 is correct

Answer:

Step-by-step explanation:

E D G E

Answer:

10.5

Step-by-step explanation:

Given

A = (1/4, 3)

B = (1/2, 4.5)

To get the coordinate of C as 7/4, what was done was to first take the difference in the x coordinates and then dilate the result by 7

To get the y coordinate;

Difference = 3 - 4.5

Difference = -1.5

This is done y multiplying the result by 7;

y coordinate = 1.5 * 7

y coordinate = 10.5

Hence its y-coordinate is 10.5

For x = 0, we have 4y = 12, which implies y = 3

For y = 0, we have 5x = 12, which implies x = 2.4

Since y-intercept is not an integer, we can find another point with integer coordinates by rearranging it in the standard form:

y = -5x/4 + 3

For x = 4, we have y = -2

Then, to graph the equation, we just need to draw a line passing through the points (0,3) and (4,-2)

The argument to be proven is Δ: ~(x)(Bx ⊃ Dx). This can be demonstrated using a proof by contradiction, assuming the negation of Δ and deriving a contradiction.

To prove Δ: ~(x)(Bx ⊃ Dx), we will use a proof by contradiction. We assume the negation of Δ, which is ((x)(Bx ⊃ Dx)). By double negation, this can be simplified to (x)(Bx ⊃ Dx).

Next, we will introduce a new assumption, let's call it γ, which states (∃x)(Bx • ~Dx). We will aim to derive a contradiction from this assumption.

By using the existential elimination (∃E) rule, we can introduce a specific variable, say c, such that (Bc • ~Dc) holds.

Now, we can apply the universal elimination (∀E) rule to the assumption (x)(Bx ⊃ Dx) using the variable c, which gives us Bc ⊃ Dc.

Using modus ponens, we can combine Bc ⊃ Dc with Bc • ~Dc to derive a contradiction, which negates the assumption γ.

Having derived a contradiction, we can conclude that the negation of Δ: ~(x)(Bx ⊃ Dx) is true, leading to the validity of Δ itself: ~(x)(Bx ⊃ Dx).

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The argument to be proven is Δ: ~(x)(Bx ⊃ Dx). This can be demonstrated using a proof by contradiction, assuming the negation of Δ and deriving a contradiction.

To prove Δ: ~(x)(Bx ⊃ Dx), we will use a proof by contradiction. We assume the negation of Δ, which is ((x)(Bx ⊃ Dx)). By double negation, this can be simplified to (x)(Bx ⊃ Dx).

Next, we will introduce a new assumption, let's call it γ, which states (∃x)(Bx • ~Dx). We will aim to derive a contradiction from this assumption.

By using the existential elimination (∃E) rule, we can introduce a specific variable, say c, such that (Bc • ~Dc) holds.

Now, we can apply the universal elimination (∀E) rule to the assumption (x)(Bx ⊃ Dx) using the variable c, which gives us Bc ⊃ Dc.

Using modus ponens, we can combine Bc ⊃ Dc with Bc • ~Dc to derive a contradiction, which negates the assumption γ.

Having derived a contradiction, we can conclude that the negation of Δ: ~(x)(Bx ⊃ Dx) is true, leading to the validity of Δ itself: ~(x)(Bx ⊃ Dx).

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Answer:

1. Vertical: 70

2. Vertical angles

3. Adjacent angles

Explanation:

Tell whether the angles are adjacent or vertical. Then find the value of x.

The angles are vertical because they are across from each other and if you add them up the do not make 180 degrees, unless the angles were 90 degrees.

What kind of angle pair does the green angles create?

Vertical angles. This is because they are directly across from each other.

What kind of angle pair does the blue angles create?

Adjacent angles. This is because when added together they equal 180 degrees across a straight line.

Answer:

The length would just be 18

Step-by-step explanation:

Since 2 9 cm ones are joined together, the length would be 2 * 9 = 18.

Answer:

1

Step-by-step explanation:

Divide 12 in to 12 separate groups and you get 1 group of 12.

Answer:

1

Step-by-step explanation:

Answer:

Answer is A

Step-by-step explanation:

(x,y) → (x + 2, y - 8)

when moving to the right 2 the x coordinate increases by two when moving down 8 the y coordinate decreases by eight

Answer:

A0.15

Step-by-step explanation:

Answer:

3.36:45=0,8

4.40:32=1,25

536:45=0,8

6.48:50=0,96

Hope it helps and likes it

Step-by-step explanation:

3- sin Z = opp/hyp

  sin Z = 27/45

   Z = sin-¹(27/45)

   Z = 37

4- tan C = opp/adjacent

   tanC = 24/32

   C = tan -¹ ( 24/32)

   C = 36.87 ( or 37)

5-  cos X = adj/hyp

    cos X= 36/45

    X = cos-¹ (36/45)

   X = 37

6- sin C = opp/hyp

   sin C = 14/48

   C = sin -¹ (14/48)

   C= 17  (or 16.96)

Step-by-step explanation:

the radius of the circle is 10 in.

so, what is the area of the whole circle (which represents an angle of 360°) ?

the area of the circle is

pi×r² = pi×10² = 100pi

ok, now we don't need the area of the full 360°. we only need the area of 120°.

what would be the area of only 1° ?

I think that is fully clear : it would be the area of the full circle divided by 360 :

100pi / 360

and now, based on this, what is then the area of 120° ?

well, 120 times the area of 1° :

(100pi / 360) × 120 = 100pi × 120/360 = 100pi × 1/3 =

= 100pi/3 = 104.7197551... in² ≈

≈ 104.72 in²

so, you see, the area of a sector is always the area of the full circle multiplied by (angle/360).

the sector is nothing else than a fraction of the full circle.

take the natural logarithm of both sides:

Divide both sides by ln(12):

Answer:

58.3°

Step-by-step explanation:

Missing Information:

In this question the diagram is missing Following are the attachment of diagram of the given question.

As we seen that the vertex c is making the right angle i,e 90°  also there is an acute angle the Hypotenuse: 20 cm and the perpendicular is 10.5 cm

Now we have find the best approximation of the angle ABC used the cosx  trigonometric function.

\(cos\ x\ =\ \frac{perpendicular}{Hypotenuse} \\\)

Putting the value of perpendicular and hypotenuse in the previous formula we get

\(cos\ x\ =\ \frac{10.5\ cm}{20\ cm} \\\)

\(x\ =cos^{-1}\ 0.525\\x \ = \ 58.33\)

Answer:

58.3

Step-by-step explanation:

jus did the test review on EDGE! :)

The method used to assign probabilities when the results of experimentation or historical data are used to assign probability values is referred to as the relative frequency method.

The relative frequency method is a way to assign probability values to events based on how often they have occurred in the past.

The probability of an event is determined by counting the number of times the event has occurred in a given set of observations, and dividing that number by the total number of observations. For example, if a certain event has occurred 20 times out of 100 total observations, the probability of that event would be 0.2 (20/100). This method is based on the idea that the probability of an event is related to its frequency of occurrence in a large number of trials.

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Answer:

What you need help on?

Step-by-step explanation:

Found that a short stanza contains 8 lines and a long stanza contains 9 lines.

What is linear equation ?

A linear equation is an equation that describes a straight line in a two-dimensional coordinate system. The general form of a linear equation is:

y = mx + b

Explanation:
Let's use "s" to represent the number of lines in a short stanza and "l" to represent the number of lines in a long stanza.

From the problem, we know that Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. This can be written as the equation:

10s + 2l = 98

We also know that Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. This can be written as the equation:

3s + 7l = 87

We want to find the values of s and l that satisfy both of these equations. We can use algebra to solve for s and l.

Multiplying the first equation by 3, we get:

30s + 6l = 294

Multiplying the second equation by 2, we get:

6s + 14l = 174

Now we can add the two equations together to eliminate the variable s:

30s + 6l + 6s + 14l = 468

Simplifying and rearranging, we get:

36s + 20l = 468

Dividing both sides by 4, we get:

9s + 5l = 117

Now we have a new equation that relates the values of s and l that satisfy both sets of stanzas. We can use this equation along with one of the original equations to solve for either s or l.

Let's use the first equation, 10s + 2l = 98. We can solve for s in terms of l:

10s + 2l = 98

10s = 98 - 2l

s = (98 - 2l)/10

Now we can substitute this expression for s into the equation 9s + 5l = 117:

9[(98 - 2l)/10] + 5l = 117

Simplifying and solving for l, we get:

l = 9

Now we can substitute this value of l back into either of the original equations to solve for s. Using the first equation:

10s + 2l = 98

10s + 2(9) = 98

10s = 80

s = 8

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The answer to the probability that 113 or fewer people in this sample have had chickenpox in their childhood is 0.1422

The probability that 113 or fewer people in this sample have had chickenpox in their childhood is 0.1422(rounded to four decimal places).

Step-by-step explanation : We can use the binomial probability formula to solve this problem.                                                                     Let's assume p be the probability that a person had chickenpox in their childhood.                                                                                  q = 1 - p is the probability that a person did not have chickenpox in their childhood.                                                                                           n is the sample size which is 400.                                                                                                                                                                                                                                                                             The formula is as follows:P(X ≤ 113) = P(X = 0) + P(X = 1) + ... + P(X = 113)P(X = k) = C(n, k) * p^k * q^(n-k) where C(n, k) is the combination of n objects taken k at a time which is given by n!/k!(n-k)! Substituting the values of n, p, q, and k in the formula we get, P(X ≤ 113) = ∑ C(400, k) * p^k * q^(n-k) , for k = 0 to k = 113.

We can calculate the probability  using a calculator or Microsoft Excel.

Using the Excel formula = BINOM.DIST(113,400,0.17,TRUE) we get the answer as 0.1422(rounded to four decimal places).Therefore, the probability that 113 or fewer people in this sample have had chickenpox in their childhood is 0.1422 (rounded to four decimal places).

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Answer:

3 Whole pieces

Step-by-step explanation:

A turkey was cut into 10 equal pieces.

For Katie

If Katie ate 2/10 of the turkey

Number of Whole pieces of turkey Katie ate =

2/10 × 10 whole pieces = 2 whole pieces

For Lorenzo

Lorenzo ate 5/10 of the turkey

Number of Whole pieces of turkey Lorenzo ate =

5/10 × 10 whole pieces = 5 whole pieces

how many whole pieces of the turkey are left?

This is calculated as:

10 pieces - (2 piece + 5 pieces)

10 pieces - 7 pieces

= 3 pieces

Therefore, we have 3 whole pieces of turkey left.

Answer:

3 Whole pieces

Step-by-step explanation:

A turkey was cut into 10 equal pieces.

For Katie

If Katie ate 2/10 of the turkey

Number of Whole pieces of turkey Katie ate =

2/10 × 10 whole pieces = 2 whole pieces

For Lorenzo

Lorenzo ate 5/10 of the turkey

Number of Whole pieces of turkey Lorenzo ate =

5/10 × 10 whole pieces = 5 whole pieces

how many whole pieces of the turkey are left?

This is calculated as:

10 pieces - (2 piece + 5 pieces)

10 pieces - 7 pieces

= 3 pieces

Therefore, we have 3 whole pieces of turkey left.

The cost of 5 small greeting cards and 4 large greeting cards is given by $24.25.

Total cost of x small greeting cards and y large greeting cards is given by $(1.25x + 4.5y).

Given that the cost of each small cards = $1.25

the cost of each big cards = $4.50

So the cost of 5 small cards = $1.25*5 = $6.25

the cost of 4 large greeting cards = $4.5*4 = $18

So total cost to get 5 small greeting cards and 4 large greeting cards = 6.25 + 18 = $24.25

Cost of x small greeting cards = $1.25x

Cost of y large greeting cards = $4.5y

Total cost of x small greeting cards and y large greeting cards = $(1.25x + 4.5y).

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Using the linear equation ,

the fraction of red knights that are magical is 7/27 .

The Knights in a certain kingdom come in two colors that is red and blue .

let k be the number of knights then the number

of red knights is 2k/7 and the number of blue knights is 5k/7.

Let b be the fraction of blue knights that are magical - then 2b is the fraction of red knights

that are magical.

Also, we have total magical knights are 1/6 of total knights .

so, we can write the above statements in equation form,

b×5k/7 + 2b × 2k/7 = k/6

=> 5b/7 + 4b/7 = 1/6

=> 9b/7 = 1/6 => 9b = 7/6

=> b = 7/54

we want to find the fraction of red knights that are magical i.e 2b = 2×7/54 = 7/27

Hence, the fraction of red knights that are magical is 7/27 .

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Answer:

∠2 and ∠5

∠6 and ∠3

Step-by-step explanation:

Vertical angles are a pair of non-adjacent angles formed by intersecting two straight lines.

Looking at the options, the answers are ∠2 and ∠5, ∠6 and ∠3

Answer:

y=2x-24

Step-by-step explanation:

y--8=2(x-8)

y+8=2x-16

y=2x-24

The surface area of the composite prism is 190.8 square cm

From the question, we have the following parameters that can be used in our computation:

The composite prism

The formula for the surface area of the composite prism is calculated as

S = Surface area of cuboid + surface area of the top

Using the area formulas, we have

S = 2 * (6 * 3 + 6 * 8 + 8 * 3) + 2 * 1/2 * 2 * 3 + 8 * 3.6 - 8 * 3

Evaluate

S = 190.8

Hence, the surface area of the composite prism is 190.8 square cm

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Answer:

2 units

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangle are acute, obtuse, scalene, isosceles, equilateral and right angled triangle.

Since point D and E are midpoints of the sides of triangle ABC, hence:

AD = BD = 3t, BE = CE = 4t, AC = 7t + 6

The perimeter of triangle ABC = AC + BC + AB = AC + AD + BD + BE + CE;

Substituting:

48 = 7t + 6 + 3t + 3t + 4t + 4t = 21t + 6

48 = 21t + 6

21t = 42

t = 2 units

Answer:

1/2

Step-by-step explanation:

12 + 6 = 18

18 + 4 + 2 = 24

12/24 = 1/2

1/2 of her party guests are cousins.

Hope this helps!