The length of one of the parallel sides of a trapezium is 5 more than the other parallel side. The perpendicular height is 7 cm. Write an expression for the area

Answer:

Step-by-step explanation:

To divide two polynomials, we use the long division algorithm. This involves dividing the terms of the dividend by the terms of the divisor and then using the resulting quotient and remainder to express the original polynomial as a quotient plus a remainder.

In this case, we have the following:

5h + 9 = (h + 4)

To apply the long division algorithm, we first divide the first term of the dividend, 5h, by the first term of the divisor, h. This gives us a quotient of 5 and a remainder of 0. We then subtract this quotient from the dividend, which gives us 9. We then divide this remainder by the divisor, which gives us a quotient of 2 and a remainder of 1. We then subtract this quotient from the dividend, which gives us 0.

Therefore, the result of the division is:

5h + 9 = (h + 4) = 5h + 4h + 1 + 0

where the quotient is 5h + 4h = 9h and the remainder is 0.

Since the remainder is 0, the polynomial divides evenly, and the final result is:

(5h + 9) = (h + 4) = 9h + 0

Note that the remainder is usually expressed as a fraction, but in this case it is 0, so it is not necessary to include it in the final result.

The amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

Given,

Two waves are described by:

3₁ (2, 1) = (0.30) sin(5z - 200t)] and

g (z,t) = (0.30) sin(52-200t)

+ =]

where OA A, 0.52 m and v= 40 m/s

OB A=0.36 m and

v= 20 m/s OC

A=0.60 m and

v= 1.2 m/s OD.

A = 0.24 m and

v= 10 m/s

DE A=0.16 m and

= 17 m/s

The amplitude of a wave is the distance from its crest to its equilibrium. The amplitude of the resultant wave is calculated by adding the amplitudes of the individual waves and is represented by A.

The expression for the resultant wave is given by f(z,t) = 3₁ (2, 1) + g (z,t)

= (0.30) sin(5z - 200t)] + (0.30) sin(52-200t)

+ =]

f(z,t) = (0.30) [sin(5z - 200t) + sin(52-200t)

+ =]

Therefore, A = 2(0.30) = 0.60 m/s

The speed of a wave is given by the product of its wavelength and its frequency. The wavelength of the wave is the distance between two consecutive crests or troughs, represented by λ. The frequency of the wave is the number of crests or troughs that pass through a given point in one second, represented by f.

Speed = λf

The wavelengths of the given waves are OA = 0.52 m,

OB = 0.36 m,

OC = 0.60 m,

OD = 0.24 m,

DE = 0.16 m

The frequencies of the given waves are OA :

v = 40 m/s,

f = v/λ

= 40/0.52

= 77.0 Hz

OB : v = 20 m/s,

f = v/λ

= 20/0.36

= 55.6 Hz

OC : v = 1.2 m/s,

f = v/λ

= 1.2/0.60

= 2.0 Hz

OD : v = 10 m/s,

f = v/λ

= 10/0.24

= 41.7 Hz

DE : v = 17 m/s,

f = v/λ

= 17/0.16

= 106.25 Hz

The speed of the resultant wave is the sum of the speeds of the individual waves divided by the number of waves. Therefore,

Speed of the resultant wave = (40 + 20 + 1.2 + 10 + 17)/5

= 17.64 m/s

Hence, the amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

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The amplitude of the resultant wave and its speed are to be determined.

Let's use the formula of the resultant wave, where,

A is amplitude, f is frequency, v is velocity and λ is wavelength of the wave.

A = \([(OA^2 + OB^2 + OC^2 + OD^2 + DE^2 + 2(OA)(OB)(cosθ) + 2(OA)(OC)(cosθ) + 2(OA)(OD)(cosθ) + 2(OA)(DE)(cosθ) + 2(OB)(OC)(cosθ) + 2(OB)(OD)(cosθ) + 2(OB)(DE)(cosθ) + 2(OC)(OD)(cosθ) + 2(OC)(DE)(cosθ) + 2(OD)(DE)(cosθ))]^{1/2\)

where, cosθ = [λ1/λ2] and λ1, λ2 are the wavelength of the two waves.

The velocity of the wave is given by the relation v = fλ

We can calculate the velocity of the resultant wave by using the above formula and calculating the value of wavelength of the wave.

Here, we are given λ for each wave. Speed = 40 m/s

Amplitude of the resultant wave= \([ (0.52^2 + 0.36^2 + 0.6^2 + 0.24^2 + 0.16^2 + 2(0.52)(0.36) + 2(0.52)(0.6) + 2(0.52)(0.24) + 2(0.52)(0.16) + 2(0.36)(0.6) + 2(0.36)(0.24) + 2(0.36)(0.16) + 2(0.6)(0.24) + 2(0.6)(0.16) + 2(0.24)(0.16) )]^{1/2\)

=\([ (0.2704 + 0.1296 + 0.36 + 0.0576 + 0.0256 + 0.3744 + 0.624 + 0.2496 + 0.1664 + 0.1296 + 0.0864 + 0.0576 + 0.144 + 0.096 + 0.0384) ]^{1/2\)

=\([ (2.2768) ]^{1/2\)

= 1.51 m/s

Therefore, the amplitude of the resultant wave is 1.51 m/s and the speed of the wave is 1.51 m/s.

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Answer:

2(3x^2+3x+1)

Step-by-step explanation:

Answer:

(6x^2) + (6x + 1)

Step-by-step explanation:

We know perimeter is the sum of all sides of an object, so in this case, we can write it like this:

3x + 1 +3x + 1 + 3x^2 + 3x^2

Now we simplify:

2(3x+1) + 2(3x^2)

(6x^2) + (6x + 1)

Answer:

C

Step-by-step explanation:

as it goes 4.66666666... forever.

A is just a rounded answer.

B would mean 4.6767676767...

and D is just truncated.

The z-transform of the sequence {coshαn} is given by Z{coshαn} = \(1/(1 - e^αz + e^(-αz)).\)

To find the z-transform of the sequence {coshαn}, we can use the formula for the z-transform of a sequence defined by a power series. The power series representation of coshαn is coshαn = \(1 + (αn)^2/2! + (αn)^4/4! + ... = ∑(αn)^(2k)/(2k)!\), where k ranges from 0 to infinity.

Using the definition of the z-transform, we have Z{coshαn} = ∑(coshαn)z^(-n), where n ranges from 0 to infinity. Substituting the power series representation, we get Z{coshαn} = \(∑(∑(αn)^(2k)/(2k)!)z^(-n).\)

Now, we can rearrange the terms and factor out the common factors of α^(2k) and (2k)!. This gives Z{coshαn} = \(∑(∑(α^(2k)z^(-n))/(2k)!).\)

We can simplify this further by using the formula for the geometric series ∑(ar^n) = a/(1-r) when |r|<1. In our case, a = α^(2k)z^(-n) and r = e^(-αz). Applying this formula, we have Z{coshαn} = \(∑(α^(2k)z^(-n))/(2k)! = 1/(1 - e^αz + e^(-αz)), where |e^(-αz)| < 1.\)

In summary, the z-transform of the sequence {coshαn} is given by Z{coshαn} = \(1/(1 - e^αz + e^(-αz)).\)

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Answer:

44:1

Step-by-step explanation:

220:5

44:1

divide by 5 each side

Pls mark as brainliest

Answer:

5<x<19

Step-by-step explanation:

Answer

The value of the function at x = 5 is 486.

We have,

The given function is f(x) = 2(3)x, which means that for any value of x, the output or the value of the function f(x) is obtained by raising 3 to the power of x, then multiplying the result by 2.

To find the value of f(5),

We simply substitute x = 5 into the function expression and simplify:

\(f(5) = 2(3)^5\)

f(5) = 2 x \(3^5\)

f(5) = 2 x 3 x 3 x 3 x 3 x 3

f(5) = 2 x 243

f(5) = 486

Therefore,

The value of the function at x = 5 is 486.

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Answer:

38

Step-by-step explanation:

The first term of the given sequence is 9.

The second term is 13

= 9 + 4 . = 9 + 2 × 2.

The next number is 22.

= 13 + 9 . = 13 + 3 × 3 .

In the same way the next number of the given sequence will be

22 + 4 × 4 .

= 22 + 16 = 38.

Answer:

you kinda cute ngl...

Step-by-step explanation:

Answer:

the square means those to lines make a 90 degree angle aka. right angle

Step-by-step explanation:

Answer:

Sine of x = \(\frac{\sqrt{288} }{18}\)

Cos of x = 6 / 18

Step-by-step explanation:

To solve this:

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle:

\(a^{2} + b^{2} = c^{2}\)

In any right angled triangle, for any angle:

The sine of the angle = the length of the opposite side / the length of the hypotenuse

The cosine of the angle = the length of the adjacent side / the length of the hypotenuse

In this right triangle, we know the opposite side is \(\sqrt{288}\), the adjacent side is 6, and the hypotenuse is 18

So to find the sine of x, we would do \(\frac{\sqrt{288} }{18}\)

And to find the cos of x, we would do 6 / 18

Hope this helps!! Pls mark as brainliest, ty.

Answer:

check the file above and got any confusion then comment it .

hope this helped you,

Using the normal approximation to the binomial, it is found that there is a 35.57% probability that the number of individuals in Lance's sample is.

In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:

z = x - \(\mu\)/ \(\sigma\)

Normal Probability Distribution measures how many standard deviations the measure is from the mean.  

In this problem:

The proportion of young adults ages 20–39 who regularly skip eating breakfast is given as 0.238, hence p = 0.238

A sample of 500 hence n = 500

The mean and the standard deviation are given by:

\(\mu\) = 500 ( 0.238) = 119

\(\sigma\) = 9.5225

The probability that the number of individuals in Lance's sample who regularly skip breakfast will be greater than 122, using continuity correction, then the p-value of Z when X = 122.5.

z = x - \(\mu\)/ \(\sigma\)

z = 122.5 - 119/ 9.5225

z = 0.37

Then p-value of 0.6443.

1 - 0.6443 = 0.3557.

0.3557 = 35.57%is the probability that the number of individuals in Lance's sample who regularly skip breakfast is greater than 122.

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Answer:

7.02

Step-by-step explanation:

\(\frac{18}{100}\) x 39 = 7.02

First write 18% as a decimal by moving the

decimal point two places to the left to get .18.

Next, the word "of" tells us we need to multiply.

So we multiply (.18)(39) to get 7.02.

So 7.02 is 18% of 39.

Answer:

Kimberly has $11.28 left

Step-by-step explanation:

$20.95 - $9.67 = $11.28

The number of distinct functions of the form f: [p..q] → [p..q] such that f(x) < r for all r in the domain is (q-p+1)^(q-p)

.Explanation:

Given that p and q are integers with p > q, the number of integers in the domain of f is q + p + 1, which can be written [p..q]. Let's first consider the case of just one number, say q.

For any such function, the only question is what f(q) is. There are q-p+1 choices for f(q) (p, p+1,..., q-1, q). We can write it like this:f(q) = p, orf(q) = p+1, or…,or

f(q) = q-1, or f(q) = q.This means that for every integer in the domain, we have q-p+1 choices for what the function does at that integer.

In other words, the function can take any of the q-p+1 values in the range [p, q].

Therefore, there are (q-p+1) (q-p) distinct functions of the form f: [p..q] [p..q].

Therefore, the answer is (q-p+1) (q-p).

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#1

Current temperature=0°C

Temperature before 1 hour

\(\\ \sf{:}\dashrightarrow 0+3°C=3°C\)

#2

Temperature before 3h

\(\\ \sf{:}\dashrightarrow 0+3(3)=0+9=9°C\)

#3

Temperature before 4.5h

\(\\ \sf{:}\dashrightarrow 0+4.5(3)=13.5°C\)

Answer:

17.74

Step-by-step explanation:

Rounded to the nearest 0.01 or

the Hundredths Place.

Answer:

1.how many halves are in 8

2.16

Step-by-step explanation:

I did it on edge

Answer:

what they said ^^

Step-by-step explanation: have a good day and a merry christmas

Answer:

y=0

Step-by-step explanation:

The population mean pulse is approximately 70.44 beats per minute. The mean pulse of sample 1 is approximately 65 beats per minute.

The mean pulse of sample​ 2, is approximately 73.67 beats per minute.

a. mean = ∑x/n

= 634 / 9

= 70.44

b. The mean of sample 1

= 64 + 65 + 66 / 3

= 195 / 3

= 65

c. the mean of sample 2

= 81 + 67 + 73 / 3

= 221 / 3

= 73.67

In summary,  The population mean pulse is approximately 70.44 beats per minute. The mean pulse of sample 1 is approximately 65 beats per minute. The mean pulse of sample​ 2, is approximately 73.67 beats per minute.

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Complete question

Student

Pulse

Perpectual Bempah

64

Megan Brooks

81

Jeff Honeycutt

67

Clarice Jefferson

68

Crystal Kurtenbach

80

Janette Lantka

70

Kevin McCarthy

73

Tammy Ohm

65

Kathy Wojdya

66

(a) Determine the population mean pulse is approximately ____?__beats per minute.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

​(b) Determine the sample mean pulse of the following two simple random samples of size 3.

Sample​ 1: {Perpectual, Tammy Kathy}

Sample​ 2: {Jeff, Megan, Kevin}

The mean pulse of sample 1 is approximately ___?___ beats per minute.

​(Round to the nearest tenth as​ needed.)

The mean pulse of sample​ 2, is approximately ____?__ beats per minute.

​(Round to the nearest tenth as​ needed.)

The value of state price λ(2,0) is 0.18.

In a two-step model with R = 1.2, if one state price is λ(2,2) = 0.18, the state price λ(2,0) can be determined as follows: State prices are the measure of the cost of different future states of the economy. In terms of probabilities, they express the likelihood that the economy will experience different future states. The state price λ is defined as follows:

λ = (1 + R) / R^(n+1)

where R is the gross risk-free interest rate,

n is the number of periods to maturity and

λ is the state price for that maturity.

λ(2,2) = 0.18 can be rewritten as follows: 0.18 = (1 + 1.2) / 1.2^(2+1)

Simplifying:0.18 = 2.64 / 1.728

Thus, λ(2,2) = 0.18 means that λ = 0.06 for the first period and λ = 0.12 for the second period.

Using the two-state model, the state price λ(2,0) can be determined as follows:

λ(2,0) = λ(2,2) x (1 + R)^(n-2) = λ(2,0) = 0.18 x (1 + 1.2)^(2-2) = λ(2,0) = 0.18 x 2.2^0 = λ(2,0) = 0.18 x 1

λ(2,0) = 0.18

Thus, the value of state price λ(2,0) is 0.18.

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The equation to illustrate a word problem regarding the renting of a car is 60 + 3h.

It should be noted that an equation is simply used to illustrate the information given about the variables.

An example of word problem simply that can be illustrated by an equation will be that the initial deposit to rent a car is $50 and there's an hourly rate of $3.

Therefore, based on the above information, the equation to illustrate this will be:

= Initial cost + Hourly rate

Let the number of hours be represented by h.

= 50 + (3 × h)

= 50 + 3h

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To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

The linear function y = 48x represents the distance y, given x gallons.

The domain is an infinite positive values of x, that is x can be represented by all positive numbers. Hence the domain is continuous