Work out
√18 - 28/√50
Give your answer in the form
√a/b
where a and b are integers.

The teacher has to select four members out of a math club of twelve members. There are 495 possible ways for her to make the selection.

To determine the number of ways the teacher can select four members from a math club of twelve, we can use the concept of combinations. A combination is a selection of items without regard to the order in which they are chosen. In this case, the teacher needs to select four members, and the order in which they are chosen does not matter.

The formula for calculating combinations is given by "n choose k," which is denoted as C(n, k) or nCk. In this case, the teacher needs to choose four members out of twelve, so the calculation would be 12C4.

Using the formula for combinations, 12C4 = 12! / (4!(12-4)!), where "!" represents the factorial function. Simplifying the expression gives us 12! / (4!8!).

The factorial function represents the product of all positive integers up to a given number. So, 12! is equal to 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Simplifying further, we have 12! / (4!8!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1).

Calculating the expression gives us (11880) / (24) = 495.

Therefore, there are 495 possible ways for the teacher to make her selection of four members from the math club of twelve.

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The Graham's scan algorithm calculates the convex hull of a set of points, which guarantees a convex polygon. The smallest area polygon containing the set of points is not the convex hull of those points.

To demonstrate that the smallest area polygon containing a set of points may not always be a convex hull of that set of points, let's consider a simple example.

Suppose we have a set of four points: A, B, C, and D, arranged in a square formation, as shown below:

A----B

|    |

|    |

D----C

If we calculate the convex hull of these points using the Graham's scan algorithm, we would obtain the convex hull as ABCDA, which is a square.

However, if we look for the smallest area polygon that contains these points, we can find a non-convex polygon. By connecting the points A, B, C, and D in that order, we form a quadrilateral:

A----B

\  /

 \/

 /\

/  \

D----C

This quadrilateral, ABCD, is not convex, as it has an internal angle greater than 180 degrees.

Hence, in this example, the smallest area polygon containing the set of points is not the convex hull of those points. This example demonstrates that the smallest area polygon can be non-convex, and the convex hull may not always provide the minimum area solution.

The Graham's scan algorithm specifically calculates the convex hull of a set of points, which guarantees a convex polygon. However, to find the smallest area polygon, other techniques or algorithms need to be applied.

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the radius of the circle is 30 cm when the circumference is 188.4 . The length of the boundary is its circumference.

A boy has traveled a certain distance if, after sprinting around the park once, he arrives at point "A" from point "A" in the first place. The park's circumference, which has the shape of a circle, is the length or border that it encompasses. The length of the boundary is its circumference.

calculation

Circumference=2πr

188.4=2×3.14×r

188.4=6.28×r

r= 188.4/6.28

radius=30cm

the radius of circle is 30 cm when the circumference is 188.4 .

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The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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There are 12 possible seating arrangement that Ali, Bonnie, Carlo, and Dianna can seat in a 4 seated car while visiting to a nearby theme park.

There are in total 4 people so the the possible seating arrangement should be 4! = 4*3*2 = 24.

But only 2 people know how to drive a car that is Bonnie and Carlo,

So the remaining seat can be occupied by any three that are remaining beside the driver.

So 3 remaining people can go in the front passenger seat.

There are 2 people who can go in the first back passenger seat.

The remaining person must go in the last seat.

Thus, there are 2x3x2 or 12 ways that they can be seated.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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Answer:

12 units

Step-by-step explanation:

The side that is on the opposite side of the triangle as angle C is the side labeled as 12 units in length

Base 10 blocks are used to perform arithmetic operations.

To model the product of 3 and 0.51, Evan needs 3 copies of 5 tenths and 1 hundredths.

What are base - 10 blocks?

Base 10 blocks are a collection of four distinct types of building blocks that, when combined, can assist you in visualizing and comprehending the appearance and value of a number. In addition, base 10 blocks can be utilized to comprehend volume, perimeter, area, multiplication, division, and addition and subtraction.

Given: Evan used base-10 blocks to model the product of 3 and 0.51.

We have to find how can Evan use this model to determine the product.

Consider the expression for product of 3 and 0.51 as,  3 x 0.51

Express 0.51 as 0.5 + 0.01

3 x 0.51 = 3 x (0.5 + 0.01)

Hence, Evan needs 3 copies of 5 tenths and 1 hundredths.

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The height of the lean-to on its vertical side is 8 feet.

To find the height of the lean-to on its vertical side, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the vertical side is the hypotenuse, and the length and width are the other two sides.

So, we have:

\(height^2 = hypotenuse^2 - width^2\)

We know the length of the roof (the hypotenuse) is 17 feet, and the width is 15 feet. So we can plug these values into the equation and solve for the height:

\(height^2 = 17^2 - 15^2\\height^2 = 289 - 225\\height^2 = 64\\height = 8\)

Therefore, the height of the lean-to on its vertical side is 8 feet.

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To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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If there's a diameter of 14 feet, then the radius is 7 feet because it's half.

The volume would be

Where r = 7, so

For a binomial random variable X with an expected value of 6 and a variance of 2.4, we can calculate the probability P(X = 5) = 0.2744 and the expected value \(E(3X^2 - 4X + 5)\) approximately equal to 101.2.

Given that X is a binomial random variable, the expected value (μ) is equal to np and the variance (σ^2) is equal to np(1-p), where n is the number of trials and p is the probability of success.

From the given information, we have μ = 6 and σ^2 = 2.4. To find the values of n and p, we can set up the following equations:

μ = np = 6, σ^2 = np(1-p) = 2.4. Solving the first equation for p, we get p = \(\frac{6}{n}\). Substituting this into the second equation, we have:

2.4 = \(\frac{6}{n} * \frac{1-6}{n}\). Simplifying and rearranging the equation, we get:

2.4n = \(6^{2}\) \(- 6n\). Solving for n, we find n = 9.

Substituting the value of n back into p = \(\frac{6}{n}\), we get p = \(\frac{6}{9}\) = \(\frac{2}{3}\).

a. P(X = 5) is calculated using the binomial probability formula:

P(X = 5) = (9 choose 5) * \(\frac{2}{3}^{5} * \frac{1}{3} ^{4}\), where (9 choose 5) represents the binomial coefficient.

Calculating this expression, we find P(X = 5) = 0.2744.

b. E\((3X^2 - 4X + 5)\) is the expected value of the expression \(3X^2 - 4X + 5\).

Using the linearity of expectation, we can break down this expression:

E\((3X^2 - 4X + 5)\) = \(3E(X^2) - 4E(X) + 5\).

The expected value of X is E(X) = μ = 6, which we were given.

To find \(E(X^2)\), we use the relationship \(E(X^2)\) = \(Var(X) + [E(X)]^2\).

Given that Var(X) = σ^2 = 2.4, we have \(Var(X) + [E(X)]^2 = 2.4 + 6^2\)  = 2.4 + 36 = 38.4. Substituting these values into the expression, we find:

\(E(3X^2 - 4X + 5)\) = 3(38.4) - 4(6) + 5 = 101.2. Therefore, \(E(3X^2 - 4X + 5)\)is approximately equal to 101.2.

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Answer:

Step-by-step explanation:

Let's make a proportion:

5 min piano   -      8 min gitar

X min piano   -     64 min gitar

Olumide practice pian:

\(X=\frac{5 \cdot 64 }{8} = 40 min\)

Given:

The set is

\(\{(3,4),(4,4),(8,-1)\}\)

To find:

The correct option for the given set which represents the quality that is not in the given set.

Solution:

We have,

\(\{(3,4),(4,4),(8,-1)\}\)

It is the set of ordered pairs. So, it is a relation.

For each x-value there is a unique y-value value. So, it is a function.

All elements are real numbers but they not distinct and they are in ordered pairs. So, the given set is not a set of real numbers.

In one to one functions each image has exactly one preimage and each preimage has exactly one image.

In the given set 4 has two preimages 3 and 4. So, the given set is not a one to one function.

Therefore, the correct options are C and D.

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

x = 6

Step-by-step explanation:

we can multiply the entire equation by 3 to simplify the numbers

-2x + 27 = 4x - 9

27 = 6x - 9

36 = 6x

x = 6

To put the equations 5x - 9 = y and 2x = 7y in matrix form, we can write them as a system of equations by rearranging the terms. The matrix form can be represented as:

| 5  -1 |   | x |   | -9 |

| 2   -7 | * | y | = |  0 |

In matrix form, a system of linear equations can be represented as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

For the equation 5x - 9 = y, we can rearrange it as 5x - y = 9. This equation corresponds to the row [5 -1]X = [-9] in the matrix form.

For the equation 2x = 7y, we can rearrange it as 2x - 7y = 0. This equation corresponds to the row [2 -7]X = [0] in the matrix form.

Combining these two equations, we can write the system of equations in matrix form as:

| 5  -1 |   | x |   | -9 |

| 2   -7 | * | y | = |  0 |

This matrix form allows us to solve the system of equations using various methods, such as Gaussian elimination or matrix inversion.

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Option A is correct.The equation for the parabola is A.(x - 3)^2 = 2(y - 2.5)

The equation for a parabola with a focus (h, k) and a directrix y = a can be expressed as:

(x - h)^2 = 4a(y - k)

The focus is (3, 4) and the directrix is y = 2, we can substitute these values into the equation:

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

Simplifying:

(x - 3)^2 = 8(y - 4)

The correct equation for the parabola is:

(x - 3)^2 = 8(y - 4)

Therefore, the answer is option A. (x - 3)^2 = 2(y - 2.5)

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By using Mai’s method, the skirt will cost $21.67, By using Elena’s method, the skirt will cost $21 and I think Mai’s method is correct.

(1) We need to find out how much the skirt cost if we use the Mai method. the Mai method is to multiply $30 by 0.80 and then we need to again multiply it with the result which can be given as,

= 30 × 0. 85 × 0. 85

= 21.67

Therefore, By using Mai’s method, the skirt will cost $21.67.

(2) We need to find out how much the skirt cost if we use Elena’s method. Elena’s method is to  multiply $30 by 0. 70 it can be given as,

= 30 × 0. 70

=$21

Therefore, By using Elena’s method, the skirt will cost $21.

(3) I think Mai’s method is correct because she took one 15% discount first and then considered the second discount which is given by the shop. whereas  Elena considered the two discounts at once and calculated it as 30% where the shop offered a 15% discount on the dress and then added a second discount on the purchase cost or bill amount that is why Mai’s method is correct.

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The amount charged by the boutique for each item is given as follows:

The price of each item is obtained considering a system of equations, for which the variables are given as follows:

From the description, the equations are given as follows:

Simplifying the first equation by 11, we have that:

3.272727x + y = 299.5454

y = 299.5454 - 3.272727x

Replacing on the second equation, the cost of a wallet is given as follows:

91x + 10(299.5454 - 3.272727x) = 7599

58.2728x = 4603.5455

x = 4603.5455/58.2728

x = 79.

Then the cost of a belt is obtained as follows:

y = 299.5454 - 3.272727(79)

y = $41.

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Answer:

A (first one)

Step-by-step explanation:

From T to T' you add 2 to the x and subtract 3 from the y

Then you do that to the x and y on O and Y

So for O, -4+2 is -2 and 1-3=-2

then you just do that for Y and you get (0,0) when applied

If you deposit $2,500 in a bank account that pays an APR of 3.55% and compounds interest monthly, after 6 years, the future value in the account will be $3,092.49.

The future value can be determined using the FV formula that compounds the present value using the FV factor as follows:

FV = PV (1 + r)^nt.

The future value can also be computed using an online finance calculator as follows:

N (# of periods) = 72 months (6 years x 12)

I/Y (Interest per year) = 3.55%

PV (Present Value) = $2,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,092.49

Total Interest = $592.49

Thus, the initial deposit of $2,500 will become $3,092.49 in 6 years at 3.55% compounded monthly.

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The number of balloons that Twinkie could pop in 1 minute is given as follows:

153 balloons.

The number of balloons that Twinkie could pop in 1 minute is obtained applying the proportions in the context of the problem.

He can pop 100 balloons in 39.08 seconds, hence the number of balloons that he can pop per second is given as follows:

100/39.08 = 2.5589 balloons per second.

Then the number of balloons in 60 seconds is given as follows:

60 x 2.5589 = 153 balloons.

(rounding down, as a bit more time than 60 seconds will be needed for the 154th balloon).

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To calculate the numerator sxx, which is part of a formula for calculating variance or sum of squares, additional information about the dataset or specific formula is needed.

The process involves finding the sum of squares of the data points by subtracting the mean from each data point, squaring the result, and summing up these squared differences. The formula used depends on the statistical method or context. Once sxx is determined, it can be used to compute the variance of the dataset. Variance measures the spread or variability of the data points around the mean and is obtained by dividing sxx by the degrees of freedom (n-1, where n is the sample size).

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Step-by-step explanation:

if u mean (x^3 -6x^2 -x- 6) then the answer is C

(6,-1,1)

..................,..........

but if u mean P(x) = x3 – 6x2 – x +62

then the answer is None of the above

-2.724

4.361+1.9328i

4.361+1.9328i

Answer:

49/16

Step-by-step explanation:

make the fraction into a mixed number then multiply have answer

Answer:

C

Step-by-step explanation:

parallel means no matter how far you stretch it the 2 lines will never touch and these 2 lines won’t EF and CD

Hopes this helps please mark brainliest

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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