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The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain • exactly one vowel? • exactly two vowels? • at least one vowel? • at least two vowels?

Answer:

12.5

Step-by-step explanation:

x= 5 when y = 12

y = 30 = 12 x 2.5 (do the same to the other number)

5 x 2.5 = 12.5

Ace C.a.r.l.o.s.

Answer:

289m = 2,890dm

Step-by-step explanation:

you multiply the meters by 10

The estimate that 2.8 million square feet of the building is used for office space is not reasonable

From the plan, the width of the building is:

Width = 230 feet

The building has a circular area, and it has four floors

So, the estimate of the building area is:

Area= 4πR²

So, we have:

Area= 4 * 3.14 * 230²

Evaluate

Area= 664424

The above value cannot be approximated to 2.8 million

Hence, the estimate used for office space is not reasonable

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The area of the rose garden is 129 sq. ft.

Consider the following diagram.

The dimensions of the rectangular garden:

length = 15 ft and width = 9 ft

Using the formula for the area of rectangle,

The area of the rectanguler garden would be,

A₁ = 15 × 9

A₁ = 135 ft²

In the center of the garden, she puts a smaller rectangular patch of grass. And the dimensions of the grass is 2 feet by 3 feet.

The area of rectangular patch is:

A₂ = 2 × 3

A₂ = 6 ft²

So, the area of the rose garden would be,

A = A₁ - A₂

A = 135 - 6

A = 129 ft²

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Find the complete question below.

5 flight attendants are required.

The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.

The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.

The number of flight attendants required can be determined by the following formula:

The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.

So, for an aircraft with 275 seats and 249 passengers:

(249 / 50) + 1

= 5 flight attendants are required.

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Answer:

x = 21

Step-by-step explanation:

Answer:

$324.19

Step-by-step explanation:

Finding the Sale Price:

475 = 100%

Sale price = 100% - 35% = 65%

Sale price = 0.65(475) = 308.75

Finding the tax:

308.75 = 100%

Tax = 5%

Sale price + tax = 105% of 308.75 or 1.05(308.75)

Total price = 324.1875

Rounded = $324.19

Price = $324.19

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-Chetan K

The integral ∫ ln(x^17)/x^2 dx converges, and its value is given by -ln(x^17)/x + 17/x + C.Therefore, the integral converges.

To determine if the integral ∫ ln(x^17)/x^2 dx converges or diverges, we need to use the integral test. The integral test states that if f(x) is a continuous, positive, and decreasing function on the interval [a, infinity), then the infinite series ∑f(n) and the improper integral ∫f(x) dx both converge or both diverge.

In this case, we have f(x) = ln(x^17)/x^2, which is continuous, positive, and decreasing on the interval [1, infinity). Therefore, we can use the integral test to determine if the improper integral ∫ ln(x^17)/x^2 dx converges or diverges.

To evaluate the integral, we can use integration by parts with u = ln(x^17) and dv = 1/x^2 dx, which gives us:

∫ ln(x^17)/x^2 dx = -ln(x^17)/x - ∫ -17/x^3 dx
= -ln(x^17)/x + 17/x + C

where C is the constant of integration.

Now, to determine if the integral converges or diverges, we need to evaluate the limit as x approaches infinity of the integrand. We have:

lim x→∞ [ln(x^17)/x^2] = lim x→∞ [(17/x) ln(x)]/x
= lim x→∞ (17/x) * lim x→∞ ln(x)/x

Since lim x→∞ ln(x)/x = 0 (which can be shown using L'Hopital's rule), the limit of the integrand is 0.

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Answer: (x+1)(x-6)

Step-by-step explanation:

The quadratic function whose zeros are 6 and - 1 will be y = x² - 5x - 6.

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We need to find a quadratic function whose zeros are 6 and - 1.

y = (x - 6) (x + 1)

The quadratic form:

y = x² - 5x - 6

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The probability of the same couple having three girls in a row is 1/8. Option B is answer.

The probability of having a girl or a boy is 1/2. Since the events are independent, the probability of having three girls in a row is (1/2) * (1/2) * (1/2) = 1/8. The same applies to having three boys in a row, which also has a probability of 1/8. Therefore, the probability of having either three girls or three boys in a row is 1/8 + 1/8 = 1/4.

Option B (1/8) is the correct answer. The probability of having three girls in a row is 1/8 because the probability of each birth being a girl is independent of the others, and the probability of a girl is 1/2. Therefore, the probability of having three girls in a row is (1/2) * (1/2) * (1/2) = 1/8.

Option B is answer.

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The proposed solution y = xr leads to r = -2 for the given differential equation.

By substituting the proposed solution y = xr into the differential equation \(x^2y'' + 5xy' + 4y = 0\), we can find the value of r that satisfies the equation.

First, we differentiate y = xr twice to find the first and second derivatives.

\(y' = rx^(r-1)\)and \(y'' = r(r-1)x^(^r^-^2^).\)

Substituting these derivatives into the differential equation, we have:

\(x^2(r(r-1)x^(^r^-^2^)) + 5x(rx^(^r^-^1^)) + 4xr = 0\).

Simplifying the equation, we get:

\(r(r-1)x^r + 5rx^r + 4xr = 0\).

Factoring out the common term \(x^r\), we have:

\(x^r(r(r-1) + 5r + 4) = 0\).

For this equation to hold true for all x, the coefficient in front of \(x^r\) must be zero. Thus, we have:

r(r-1) + 5r + 4 = 0.

Simplifying the equation further, we get:

\(r^2 - r + 5r + 4 = 0,r^2 + 4r + 4 = 0,(r + 2)^2 = 0\).

From this equation, we find that r = -2. Therefore, the proposed solution y = xr leads to r = -2 as the solution for the given differential equation.

The proposed solution method for solving differential equations is based on the assumption that the solution can be expressed in a specific form. In this case, the proposed solution y = xr assumes that the solution is a power function of x. By substituting this solution and its derivatives into the differential equation, we can determine the value of r that satisfies the equation.

The process involves substituting the proposed solution and its derivatives into the differential equation, simplifying the equation, and identifying the condition under which the equation holds true. In this case, after simplifying the equation, we obtain a quadratic equation in terms of r. Solving this quadratic equation leads to the value r = -2, which satisfies the original differential equation.

The proposed solution method is a powerful technique used in solving linear homogeneous differential equations, where the equation can be expressed as a linear combination of the derivatives of the dependent variable with respect to the independent variable. By substituting the proposed solution, we can determine the values of the constants or exponents that satisfy the equation and find the general solution.

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Answer:

The average speed was about 6,000 kilometers (or 3,200-3,700 miles)

Step-by-step explanation:

hope this helps!

The item which is closest in size to one mole of gas at STP is C) A microwave

A mole is the quantity of matter contained in a body.

We know that at STP the volume of gas occupied by one mole of a gas at STP is 22.4 dm³.

Now, we have 4 items.

Let us assume that each item is a cube. Also, since 22.4 dm³ is the volume of the cube, its length is

L = ∛22.4 dm³

=  ∛(22.4 × 10³) cm³

= 28.2 cm

So, ithe item that is comparable to this length is the microwave.

So, the item is C. A microwave

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So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).

Answer:

Step-by-step explanation:

Answer: 65005.037

Step-by-step explanation:

I=?

P=6,500

R=037

T=5 years

 I=  6,500+037+5= 65005.037

Answer: 1.43 meters

Step-by-step explanation:

subtract 7.52 from 8.92 and that's the difference so that is how far she would have to jump to tie the record

The side length of this square is equal to 6√2 meters.

In Mathematics and Geometry, the area of a square can be calculated by using the following mathematical equation (formula);

A = x²

Where:

In Mathematics and Geometry, the side length of a square can be calculated by using this mathematical equation (formula);

Diagonal, d = √2x

By solving for the side length (x), we have:

x = d/√2

x = 12/√2

x = 6√2 meters.

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Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

The cost of petrol for the trip to UWC is R1.2384.

In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.

To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.

Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:

\(Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k\)

where k stands for liters of petrol.

To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:

\(Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters\)

Now we can calculate the cost of petrol for the trip:

\(Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384\)

Therefore, the cost of petrol for the trip to UWC is R1.2384.

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Answer:

volume = 14,137

Step-by-step explanation:

radius is the diameter divided by 2

30÷2=15

radius = 15 then square

15^2 = 225

formula of volume of a cone is 1/3*pi*raduis^2*the height

1/3(3.14)(225)(60)= 14,137

The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.

The volume of the cone is given by;

\(\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where;\ r = radius \ and \ h = height\)

The volume of a cone with a diameter of 30 feet and a height of 60 feet.

The radius of the cone is;

\(\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{30}{2}\\\\Radius=15\)

Substitute all the values in the formula

\(\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times 3.14 \times 15^2 \times 60\\\\Volume \ of \ cone=14130\)

Hence, the volume of a cone with a diameter of 30 feet and height of 60 feet is 14130.

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Answer:

3

Step-by-step explanation:

(8y-3)+(-8y+6)=

8y + -8y = 0

-3 + 6 = 3

0 + 3 = 3

Y has the largest variance = 12 (incorrect)b) Z has the largest variance = 6 (correct)c) W has the largest variance = 0 (incorrect)d)

They all have the same variance = Not correct

Given that 1,2,3,4 be independent and equally distributed random variables with expected value 0 and variance 3.

Three new random variables, Y, Z and W are defined as:Y = 1 + 2 + 3 + 4Z = 21 + 22W = 41

Now,Mean of Y = 1 + 2 + 3 + 4 = 10.

Mean of Z = 21 + 22 = 43

Mean of W = 41

As 1,2,3,4 are independent and equally distributed, then we have

                                  Variance of each of them = 3

                         Variance of Y can be calculated as follows:

                        Var(Y) = Var(1+2+3+4) = Var(1) + Var(2) + Var(3) + Var(4)

Since all are identically distributed soVar(Y) = 3 + 3 + 3 + 3 = 12

Similarly, the variance of Z and W can be calculated as follows:

                                     Var(Z) = Var(21 + 22) = Var(21) + Var(22)

Since all are identically distributed soVar(Z) = 3 + 3 = 6Var(W) = 0

The following statements can be made:

a) Y has the largest variance = 12 (incorrect)b) Z has the largest variance = 6 (correct)c) W has the largest variance = 0 (incorrect)d)

They all have the same variance = Not correct

So the correct option is (b). Therefore, Z has the largest variance.

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Answer:

The dog drank 5/12 of the bowl

Step-by-step explanation:

Common denominator

3/4 = 9/12

1/3 = 4/12

9/12 - 4/12 = 5/12

Answer: Your dog drank 5/12 of the bowl.

Step-by-step explanation:

3/4 - 1/3 = 5/12

3/4 = 9/12

1/3 = 4/12

9/12 - 4/12 = 5/12

Therefore, your dog drinks 5/12 of the water in the bowl.

hope this helps :D

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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Answer: m * 4/7 > 12/5

Answer:

29

Step-by-step explanation:

There would be 29 highways connecting 2 cities

To return an int with every 4th bit set to 1, we use a binary number that has all its 4th bits set to 1s and 0s everywhere else.

This can be done by creating a hex number where each hex digit has the MSB = 1 and all other bits as 0.

In this case, we are to set every 4th bit to 1 and return the integer. We will use a hex number to represent the binary representation of the integer. We can create a hex number where each hex digit has the MSB=1 and all other bits as 0 since the legal ops allow us to perform bitwise manipulation operations.

Here is how we can solve the problem: int fourth Bits(void){ return 0xAAAAAAAA; }

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If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.

Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.

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