What percentage of the data values represented on a box plot falls between the minimum value and the lower quartile?

a. By the binomial theorem,

[tex]\displaystyle\left(x^2+\frac1x\right)^n=\sum_{k=0}^n\binom nk(x^2)^{n-k}\left(\frac1x\right)^k=\sum_{k=0}^n\binom nkx^{2n-3k}[/tex]

which produces a constant term when [tex]2n-3k=0[/tex], or [tex]2n=3k[/tex]. [tex]2n[/tex] is even for any choice of [tex]n[/tex], so [tex]n[/tex] must be any positive integer for which [tex]2n[/tex] is an even multiple of 3 i.e. a multiple of 6. Then [tex]n[/tex] can be any of the integers in the sequence {6, 12, 18, ...}.

b. Let [tex]n=6m[/tex] for some positive integer [tex]m[/tex]. Then

[tex]\displaystyle\left(x^2+\frac1x\right)^{6m}=\sum_{k=0}^{6m}\binom {6m}k(x^2)^{6m-k}\left(\frac1x\right)^k=\sum_{k=0}^{6m}\binom{6m}kx^{12m-3k}[/tex]

and the constant term occurs when [tex]12m-3k=0[/tex], or [tex]4m-k=0[/tex], or [tex]k=4m[/tex]. At this value of [tex]k[/tex], we get the term

[tex]\dbinom{6m}{4m}x^{12m-3(4m)}=\dfrac{(6m)!}{(4m)!(6m-4m)!}=\dfrac{(6m)!}{(4m)!(2m)!}[/tex]

Answer:

As long as you mistyped Rashid's work and meant that the answer was 3/36 or 1/12, the answer would be

A. Rashid solved the problem correctly

Step-by-step explanation:

When you are dividing, it is the same thing as multiplying by the reciprocal of that value. This means that

[tex]\frac{\frac{3}{4} }{9} =\frac{3}{4} *\frac{1}{9} =\frac{1}{12}[/tex]

bro this is middle school work, its B

Answer:

x = 2[tex]\sqrt{34}[/tex]

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, thus

x² = 6² + 10² = 36 + 100 = 136

Take the square root of both sides

x = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = 2[tex]\sqrt{34}[/tex]

Answer:

2√34

Step-by-step explanation:

6² + 10² = x²

x² = 6² + 10²

x² = 36 + 100

x² = 136

x = √136

x = 2√34

Answer:

its b

Step-by-step explanation:

Answer:

B) 0.17

Step-by-step explanation:

c is the correct answer i believe

Final answer:

To find the number of friends when 36 apples are shared with each friend getting 2 apples, divide the total apples by the number of apples each friend gets. The equation to solve for the number of friends, n, is n = 36 / 2 = 18.

Explanation:

To solve for the number of friends, n, sharing 36 apples when each friend gets 2 apples:

Identify the total number of apples = 36 and the number of apples each friend gets = 2.

Divide the total apples by the apples each friend gets: 36 ÷ 2 = 18, which represents the number of friends (n). So, the equation would be n = 36 / 2 = 18.

Answer:

No, no, yes, no

Step-by-step explanation:

The first one is not random.  He is sampling only the earliest gym goers.

The second one is not random.  He is sampling only from one zip code.

The third one is random.  He is using a random number generator.

The fourth one is not random.  He is sampling only volunteers.

The third is completely random. He's generating numbers with a random number generator. So yes, for the third statement and No, for the first, second, and fourth statements.

Random sampling is the method of selecting the subset from the set to make a statical inference.

An employee at a gym wants to select a random sample of gym members for a survey about their exercise habits.

The first is not a fluke. He's simply tasting the first gym attendees.

The second is not a coincidence. He's just taking samples from one zip code.

The third is completely random. He's generating numbers with a random number generator.

The fourth is not a fluke. Only volunteers are being sampled.

More about the random sample link is given below.

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Answer:

(C)

Step-by-step explanation:

Given: BC is tangent to the circle A at D.

To prove: AB is congruent to AC

Proof:

Statements                                                            Reason

1. BC is tangent to the circle A at D.                     Given

2. DB≅DC                                                               Given

3.AD⊥BC               If a line is tangent to a circle then it is perpendicular to the radius at the point of tangency.

4. ∠ADB and ∠ADC are right angles     Definition of perpendicular lines

5. ∠ADB≅∠ADC                                      Right angles are congruent

6. AD≅AD                                                Reflexive property of congruence

7. ΔADB≅ΔADC                                      SAS rule

8. AB≅AC                                                CPCTC

Hence, option (C) is correct.

Tangent to a circle is straight line just touching the circle at one point. The reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency

A line segment which touches a circle specified to only one point is called a tangent to that circle.

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

For the given case, the missing statement for the proof is:

If a line is tangent to a circle,  then it is perpendicular to the point of tangency(the point on circle where the tangent intersects it).

Hence, the reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency

Learn more about tangent here:

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Answer:

  C)  (-3, 4)

Step-by-step explanation:

Subtract the tail from the head:

  (-2, 3) -(1, -1) = (-3, 4)

The component form is (-3, 4).

The component form of the vector from (1, -1) to (-2, 3) is (-3, 4), as it reflects the changes in the x and y directions.

The correct answer is option C.

To find the component form of the vector from (1, -1) to (-2, 3), we need to calculate the change in the x-direction and the change in the y-direction. The component form of a vector is typically written as (Δx, Δy), where Δx represents the change in the x-direction, and Δy represents the change in the y-direction.

In this case, the initial point is (1, -1), and the terminal point is (-2, 3). To find Δx and Δy, we subtract the x-coordinates and the y-coordinates, respectively:

Δx = x_terminal - x_initial = (-2) - 1 = -3

Δy = y_terminal - y_initial = 3 - (-1) = 4

So, the component form of the vector is (-3, 4).

Among the answer choices:

A. (1, 0) is not the correct component form.

B. (-5, 2) is not the correct component form.

C. (-3, 4) is the correct component form.

D. (-1, 2) is not the correct component form.

The correct answer is C, (-3, 4), which represents the change in the x-direction and the change in the y-direction as you move from (1, -1) to (-2, 3) on the graph.

Therefore, from the given options the correct one is C.

For more such information on: component form

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Answer:

$56.71

Step-by-step explanation:

with Anthony's spendings of $34.56, the 6 is in the hundredth place. If the value of the six is 100 times more in Brad's spending, the six would be in the ones place. You would move the six over two place values (because of 100) and end up with 6 dollars. If it was 10 times more, than you would only move one place value over and it would be 57.61.

Answer:

$56.71

Step-by-step explanation:

The value of the 6 in which Anthony spent is the hundredth value, or 0.06

Brad spent 100x more than the value of the digit 6 in which Anthony spent. Multiply 0.06 with 100: 100 x 0.06 = 6

6 is in the ones place value, & $56.71 is the only answer choice with 6 in the ones place value, so it is your answer.

~

Answer:

  the distance between the points is about 9.2 units

Step-by-step explanation:

It is well you should not understand it. No question is asked.

__

The answer choices suggest you are to find the distance between the two points. There is only one choice in a reasonable range: 9.2 units.

Each point is more than 2 units from any axis, so 2 units is clearly not the answer. The size of the graph is much less than 81 units, so clearly that is not the answer.

The difference of coordinates in the x-direction is 6; in the y-direction the difference is 7 units. The distance between the points will be more than the longest of these (7) and less than about 1.5 times that (10.5). Only one choice is in this range: 9.2 units.

__

The Pythagorean theorem is used to calculate the distance between points. The distance is considered to be the hypotenuse of a right triangle with legs of lengths equal to the differences of coordinates. Here, that means the distance (d) is ...

  d² = 6² + 7² = 36 +49 = 85

  d = √85 ≈ 9.2 . . . . grid squares, or "units"

Answer:

The statement which is true is, If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.

Step-by-step explanation:

In a rhombus, the diagonals bisect at perpendicular angles to form 4 triangles.Because the diagonals bisect at right angles, then it is possible to prove that the four small formed triangles are similar using the SAS theorem: two triangles are equal if two sides are equal and the angles between the two sides are equal.In your case, the sides are that on the base and that forming a height of the triangles with both having angle 90° between the sides.So you see if these the two are congruent, the hypotenuse of these triangles are congruent, making this quadrilateral a rhombus.

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Keywords : quadrilateral, rhombus, perpendicular bisector, angles

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Answer:

[tex]3\sqrt{13}[/tex]

Step-by-step explanation:

Using the Theorem of the side of a triangle:

[tex]x^2 = 4 * (4 + 9) = 42\\x = \sqrt{42}[/tex]

And using the Height Theorem:

y = [tex]\sqrt{4 \cdot 9}  = \sqrt{36} = 6[/tex]

And by the Pythagorean Therorem:

z = [tex]\sqrt{6^2 + 9^2} = \sqrt{117} = 3\sqrt{13}[/tex]

Final answer:

A triangle with sides of lengths 28, 195, and 197 satisfies the Pythagorean theorem (a² + b² = c²), which confirms it is a right triangle.

Explanation:

To determine if a triangle with sides of lengths 28, 195, and 197 is a right triangle, we can apply the Pythagorean theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the hypotenuse (the longest side) must be equal to the sum of the squares of the lengths of the other two sides.

Let us calculate:

As we can see, 784 plus 38025 indeed equals 38809. Hence, the triangle with sides 28, 195, and 197 satisfies the condition of the Pythagorean theorem and therefore is a right triangle.

Answer:

c d  a  b d

Step-by-step explanation:

Answer:

C, D, A, B, and D

Step-by-step explanation:

Answer:

6 feet

D

Step-by-step explanation:

Givens

l = 10

h = 8

w = ?

Formula

l^2 = h^2 + w^2

Solution

10^2 = 8^2 + w^2

100 = 64 + w^2

100 - 64 = 64 - 64 + w^2

w^2 = 36

sqrt(w^2) = sqrt(36)

w = 6 feet.

f(x) = /x - 2/

f(-1) = /-1 - 2/ = /-3/ = 3

f(0) = /0 - 2/ = /-2/ = 2

f(1) = /1 - 2/ = /-1/ = 1

f(2) = /2 - 2/ = /0/ = 0

Answer:  c) 3.9

Step-by-step explanation:

The mean is 95 so it has a z-score of 0

The standard deviation is 3.9 so a z-score of -1 is a velocity of 95 - 3.9

So, the difference in the their velocities is: 3.9

Final answer:

The interval estimate of the true population proportion is (0.16, 0.28) that is option D is correct.

Explanation:

The interval estimate of the true population proportion is (0.16, 0.28).

A simulation of 100 trials with a sample size of 50 was conducted to determine whether the sample supports the population proportion of 0.40. The minimum sample proportion from the simulation is 0.15 and the maximum sample proportion is 0.27. Based on this simulation, the interval estimate for the true population proportion can be calculated.

Interval estimate formula: (point estimate - margin of error, point estimate + margin of error)

Point estimate = 0.22

Margin of error = (maximum sample proportion - minimum sample proportion) / 2 = (0.27 - 0.15) / 2 = 0.06

Interval estimate = (0.22 - 0.06, 0.22 + 0.06) = (0.16, 0.28)

The correct interval estimate of the true population proportion is (0.14, 0.30).

To determine the interval estimate of the true population proportion, we use the following formula for a 95% confidence interval:

[tex]\[ \text{Confidence Interval} = \text{Point Estimate} \pm (Z_{\alpha/2} \times \text{Standard Error}) \][/tex]

where[tex]\( Z_{\alpha/2} \)[/tex] is the Z-score corresponding to the desired confidence level (for a 95% confidence interval, [tex]\( Z_{\alpha/2} \)[/tex] is approximately 1.96), and the Standard Error (SE) is calculated using the formula:

[tex]\[ \text{SE} = \sqrt{\frac{\text{Point Estimate} \times (1 - \text{Point Estimate})}{\text{Sample Size}}} \][/tex]

Given the point estimate from the simulation as 0.22 and the sample size as 50, we calculate the standard error as follows:

[tex]\[ \text{SE} = \sqrt{\frac{0.22 \times (1 - 0.22)}{50}} \] \[ \text{SE} = \sqrt{\frac{0.22 \times 0.78}{50}} \] \[ \text{SE} = \sqrt{\frac{0.1716}{50}} \] \[ \text{SE} = \sqrt{0.003432} \] \[ \text{SE} \approx 0.0586 \][/tex]

Now, we calculate the margin of error (ME):

[tex]\[ \text{ME} = Z_{\alpha/2} \times \text{SE} \] \[ \text{ME} = 1.96 \times 0.0586 \] \[ \text{ME} \approx 0.1146 \][/tex]

The margin of error is approximately 0.1146. Therefore, the 95% confidence interval for the population proportion is:

[tex]\[ \text{Point Estimate} \pm \text{ME} \] \[ 0.22 \pm 0.1146 \][/tex]

Lower bound:

[tex]\[ 0.22 - 0.1146 \approx 0.1054 \][/tex]

Upper bound:

[tex]\[ 0.22 + 0.1146 \approx 0.3346 \][/tex]

However, the simulation results provide a range for the sample proportion from 0.15 to 0.27. Therefore, the interval estimate should be adjusted to reflect this range while still incorporating the margin of error.

Lower bound (adjusted for simulation range):

[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]

Upper bound (adjusted for simulation range):

[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]

Since the lower bound of the confidence interval cannot be less than the minimum sample proportion from the simulation (0.15), and the upper bound cannot exceed the maximum sample proportion from the simulation (0.27), we adjust the interval to:

Lower bound:

0.15

Upper bound:

0.27

Now, we apply the margin of error to these bounds:

Lower bound with ME:

[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]

Since the lower bound cannot be less than 0, we round up to the nearest reasonable value, which is 0.14.

Upper bound with ME:

[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]

Since the upper bound cannot exceed 1, we round down to the nearest reasonable value, which is 0.30.

Therefore, the interval estimate of the true population proportion, taking into account the simulation results and the margin of error, is (0.14, 0.30).

A net can be used to find the area of a specific side or the entire surface area. It can also help to find the perimeter. To find the surface area with a net, solve for the area of each shape in the net and add them together to get the total area (surface area).

Hope this helps!

A flat three dimensional solid like a cube, a prism or a pyramid. When you cut out the "net", fold it and glue it together you can see what the three dimensional shape looks like. (It can be used in math)Draw a net of the polyhedron. Calculate the area of each face. Add up the area of all the faces.

Answer:

Here I leave an example that you will understand more easily  so that you understand the process better but it is easy.

First you must substitute the values ​​for the letters, and then you multiply it so basic remember to change the Pi by 3.14

Answer:

The maximum value of g(x) = 2/3 at x = 0

Step-by-step explanation:

* Lets find the maximum value of a function using derivative of it

- The function g(x) = 2/(x² + 3)

- 1st step use the negative power to cancel the denominator

∴ g(x) = 2(x² + 3)^-1

- 2nd use derivative of g(x) to find the value of x when g'(x) = 0

* How to make the derivative of a function

# If f(x) = a(h(x))^n, then f'(x) = an[h(x)^(n-1)](h'(x))

∵ [tex]g(x)=2(x^{2}+3)^{-1}[/tex]

∴ [tex]g'(x) = 2(-1)(x^{2}+3)^{-2}(2x)=-4x(x^{2}+3)^{-2}[/tex]

# Put g'(x) = 0

∴ [tex]-4x(x^{2}+3)^{-2}=0====\frac{-4x}{(x^{2}+3)^{2}}=0[/tex]

∴ [tex]-4x=(0)(x^{2}+3)^{2}====-4x = 0[/tex]

∴ x = 0

* The maximum value of g(x) at x = 0

- Substitute the value of x in g(x)

∴ g(0) = 2/(0 + 3) = 2/3

* The maximum value of g(x) = 2/3 at x = 0

Answer:

[tex]\boxed{ \text{8 p.m.}}[/tex]

Step-by-step explanation:

First, we must plot the graph of your system of equations (see below).

The two lines cross at (12, 360).

Thus, machine A had been going for 12 h. It started at 8 a.m., so it ended at 8 p.m.

Both machines had made 360 ft of wire by [tex]\boxed{ \text{8 p.m.}}[/tex]

Check:

360 = 30 × 12     360 = 40(12 – 3)

360 = 360          360 = 40 × 9

                          360 = 360

OK.

The answer would be the first option.

6.2 percent of 300 is 18.6,

and 1.45 percent of 300 is 4.35

It makes a total of 22.95

300 - 22.95 = 277.05

1014.065 hope this helps

Answer:

Step-by-step explanation:

Law of Sines.

a/sin(A) = b/sin(B)

In this case, a = y and A = 26.5. b = 15 and B = 90.

y/sin(26.5) = 15/sin(90).

y/sin(26.5) = 15/1

y = sin(26.5) * 15, which is about 6.69 feet.

The answer to your question is

6.69

Answer:

256 m²

Step-by-step explanation:

If the length of a rectangle is 4 times its width, and you know the width is 8, that must mean the length is 32. Now you know the width and the length, multiply those two values to get your area.

Answer:

It would take 13 hours

Step-by-step explanation:

522/9 = 58

754/58= 13

answer: y²-y+9

coefficient is 2

degree is 1

Answer: $1980

Step-by-step explanation:

Well, based off of the question being asked, I assume that you will need to pay $11 for 90 square footage of tiling, and then the same for the other square footage of tiling. Therefore your answer will be $1980. If you are looking for the equation, it is (11x90)=990   (990)2 = 1980

you do not need to multiply 11 by 90 again because you already know the answer.

Answer:

$110

Step-by-step explanation:

We are given that

Cost of 1 square yard of floor tile =$11

We have to find the cost of 90 square feet of tile.

To find the cost of 90 square feet we will convert it into square yard.

We know that

9 square foot=1 square yard

1 square foot=[tex]\frac{1}{9}[/tex]

90 square feet=[tex]\frac{1}{9}\times 90=10[/tex] square yard

By unitary method

Cost 1 square yard=$11

Cost of 10 square yard=[tex]11\times 10=[/tex]$110

Hence, the cost of 90 square feet to tile a bathroom=$110