in a class of 48 student,30 are boys . what is the probability that a girl is picked randomly to represent the class in a debate​

By finding the maximum number of yards, then feet, then inches, if the input is 50, then the output is 1 yard, 4 feet, and 2 inches.

To convert a length in inches to yards, feet, and inches

Note the followings:

There are 12 inches in a foot and 3 feet in a yard.

Divide the total length in inches by 36 (the number of inches in a yard) to find the number of yards, then take the remainder and divide it by 12 to find the number of feet, and finally take the remaining inches.

Given that, the input is 50 inches, the output  will be

Maximum number of yards: 1 (since 36 inches is the largest multiple of 36 that is less than or equal to 50)

Maximum number of feet: 4 (since there are 12 inches in a foot, the remainder after dividing by 36 is 14, which is equivalent to 1 foot and 2 inches)

Remaining inches: 2 (since there are 12 inches in a foot, the remainder after dividing by 12 is 2)

Therefore, 50 inches is equivalent to 1 yard, 4 feet, and 2 inches.

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The original expression simplifies to: \(5\sqrt3 + 15\sqrt2 - 2\sqrt6.\)

The aforementioned mathematical equation can be made less complex by utilizing rationalizing denominators and performing fundamental mathematical operations

Initially, simplify the denominator in every term.

For \(6/(2\sqrt3),\) multiply both the numerator and denominator by \(\sqrt3\), to get \(3\sqrt3.\)

For \(6/\sqrt(\sqrt3+\sqrt2)\), multiply both the numerator and denominator by \((\sqrt3-\sqrt2)\), to get \((\sqrt18 - \sqrt12) / 1\), which simplifies to \(3\sqrt2 - 2\sqrt3.\)

For \(4\sqrt3/(\sqrt6-\sqrt2)\), multiply both the numerator and denominator by \((\sqrt6+\sqrt2)\), to get \((4\sqrt18 + 4\sqrt6) / 4\), which simplifies to \(12\sqrt2 + 4\sqrt3.\)

Substituting these back in the original expression, we get:

\(3\sqrt3 - \sqrt6 + 3\sqrt2 - 2\sqrt3 + 12\sqrt2 + 4\sqrt3 - \sqrt6\)

This simplifies to:

\(5\sqrt3 + 15\sqrt2 - 2\sqrt6.\)

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The geometric mean of 4 and 8 is 5.7.

The geometric mean is a type of average that is calculated by taking the product of the given numbers and then finding the square root of that product. In this case, we have to find the geometric mean of 4 and 8.

To calculate the geometric mean, we multiply the given numbers: 4 * 8 = 32.

Next, we take the square root of the product: √32 ≈ 5.7.

Therefore, the geometric mean of 4 and 8 is approximately 5.7.

The geometric mean is often used to find an average when dealing with quantities that multiply together or have an exponential relationship. It is particularly useful when analyzing growth rates, ratios, or values that are inherently multiplicative. In this case, the geometric mean helps find a value that represents the "middle" or "average" of 4 and 8 in terms of their multiplication. The resulting value of 5.7 represents the common ratio between 4 and 8 that, when multiplied repeatedly, gives the same final result as directly multiplying 4 and 8 together.

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To find a function given its derivative and an initial condition, we integrate the derivative and solve for the constant using the given condition. Example: \(f(x) = 14\sqrt{x} + 12\)  satisfies  \(f'(x) = 7/ \sqrt{x}\)  and f(9) = 54.

The function f(x) can be found by integrating f'(x) with respect to x. Given \(f'(x) = 7/\sqrt{x}\), we can integrate it to obtain \(f(x) = 14\sqrt{x} + C\) , where C is an arbitrary constant.

To determine the value of C, we use the initial condition f(9) = 54, which gives us:

\(54 = 14\sqrt{9} + C\)

54 = 42 + C

C = 12

Substituting C into the expression for f(x), we get the final solution:

\(f(x) = 14\sqrt{x} + 12\)

Therefore, the function f(x) that satisfies \(f'(x) = 7/\sqrt{x}\) and f(9) = 54 is \(f(x) = 14\sqrt{x} + 12.\)

In summary, we can find a function given its derivative and an initial condition by integrating the derivative and solving for the arbitrary constant using the given condition. In this case, we found the function \(f(x) = 14\sqrt{x} + 12\) that satisfies \(f'(x) = 7/\sqrt{x}\) and f(9) = 54.

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Answer:

3,400 people

Step-by-step explanation:

First, find how many minutes are between noon and 1:30 pm

This is an hour and 30 minutes, so it will be 90 minutes

Then, multiply 90 by 35, since 35 people enter per minute

90(35)

= 3150

Then, add the 250 people that were already in it

3150 + 250

= 3400

So, there will be 3,400 people in the stadium

Answer:

3400

Step-by-step explanation:

250+35m=noon

Answer: 2x=56

Step-by-step explanation:

Answer:

The correct answer would be A.

Step-by-step explanation: Because If you look at it closly you'll see how their equivalent.

The car wash made $600 since "there will be 8 teams" meaning 8 * $75.

The length of the car wash will be five and a half hours, with two 15-minute breaks for each team.

Thus, each team works for five hours.

Two automobiles will be washed per hour by each team.

Ten vehicles per squad, then.

[5*2]

Given that "there will be 8 teams," 80 vehicles will be washed (assumed to be in a continuous line of vehicles) [10*8].

The charge must be $600/80=$7.50 each car in order to make $600.

Check (extremely important): "each crew will wash two cars per hour," meaning that each team will earn $15 per hour; "the car wash will run five and a half hours," and "each team will take two 15-minute breaks." As a result, five times $15 equals $75 earned each team.

The car wash made $600 since "there will be 8 teams" meaning 8 * $75.

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since 25 is less than 11.2, we must start putting a 0 and a comma in order to move the decimal place, like this:

then, we continue the division as usual, 112 divided by 25, 25 times 4 is equal to 100 and leaves a remainder of 12,

then, 12 is less than 25 so we put a 0 at the end and repeat the procedure on the last step,

complete the division with another 0 at the end and repeat, 25 times 8 is equal to 200 and leaves a remainder of zero.

ANSWER:

The result of the division is 0.448

$326.57 of Aly's annuity payments will be interest.

To answer these questions, we need to use the formula for the present value of an annuity, which is given by:

PV = PMT \(\times\)[1 - (1 + r\()^{(-n)\)] / r

where PV is the present value of the annuity, PMT is the payment amount, r is the monthly interest rate, and n is the total number of payments.

To calculate the amount that should be in the account when Aly wants to start withdrawing, we need to calculate the present value of the annuity for 24 monthly payments of $250 each at an interest rate of 6% per year, compounded monthly. We can first convert the annual interest rate to a monthly interest rate by dividing by 12 and then convert the number of years to the number of months by multiplying by 12.

The monthly interest rate is:

r = 0.06 / 12 = 0.005

The total number of payments is:

n = 2 \(\times\)12 = 24

The present value of the annuity is:

PV = 250 \(\times\) [1 - (1 + \(0.005)^{(-24)\)] / 0.005

= 5673.43

Therefore, Aly should have $5673.43 in her account when she wants to start withdrawing.

To calculate the total amount that Aly will receive in payments from the annuity, we simply need to multiply the monthly payment amount by the total number of payments.

The total amount of payments is:

Total payments = PMT \(\times\) n

= 250 \(\times\)24

= $6000

Therefore, Aly will receive a total of $6000 in payments from the annuity.

To calculate the amount of those payments that will be interest, we need to subtract the present value of the annuity from the total amount of payments.

The amount of interest is:

Interest = Total payments - PV

= $6000 - $5673.43

= $326.57

Therefore, $326.57 of Aly's annuity payments will be interest.

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Answer:

Step-by-step explanation:

The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means \(12^{2} +16^{2} =20^{2} -- > 144+256=400\) which is true meaning number 1 is a right triangle. \(10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25\) is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.

Answer:

x=0

Step-by-step explanation:

First distribut the 6 and 2

6x+6-5x=8+2x-2

Then put the x to one side and the coefficients to the other side

6x-2x-5x=8-2-6

Simplify

-x=0

x=0

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Answer:

How many students run TRACK? 210

How many students play BASEBALL? 98

15*14= 210 and 7*14 = 98, 210 - 98 = 112

Answer:

There are 210 students who run track and 98 students who play baseball.

Step-by-step explanation:

15x= Students who run track

7x= Students who play baseball

15x - 7x = 112 (*combine like terms)

8x = 112 (*divide 112 by 8)

X = 14 (*now plug X into both equations stated earlier)

15x = 15 x 14 = 210 (Number of students who run track

7x = 7 x 14 = 98 (Number of students who play baseball)

Answer:

11/5

Step-by-step explanation:

If you need help with more problems like this you can use m a t h w a y. (remove the spaces)  :)

Answer: 40.6Cm^3

Step-by-step explanation:

The other answer for the most part is correct, except they got the high wrong. The slant height is 8, you can figure out the actual height with the Pythagoras theorem.

a^2+b^2 = c^2

5^2 + b^2=8^2

b = square root 39

b = 6.2

The formula for a cone is: 1/3 pi*r^2*h

Now we plug in our numbers

The diameter is 5 so our radius is 2.5

Our height is 6.2

1/3 * Pi* 2.5^2 * 6.2

12.9 * 3.14

   40.6

An unreliable study can occur if the test administration is inconsistent

Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.

Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.

For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.

Therefore, a proper set schedule must be followed for the tests with consistency.

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Answer:

.

Step-by-step explanation:

Answer:

(B) (22.5, -12.5)

Step-by-step explanation:

When the point \((9,-5)\) is dilated by with a scale factor of 2.5

In a dilation, when its scale factor is less than 1, the pre-image will be lesser than the image.

However, when the scale factor is greater than 1, the pre-image will be greater than the image.

The Image of the dilation of \((9,-5)\) with a scale factor of 2.5 is therefore:

\((9*2.5,-5*2,5)\\=(22.5, -12.5)\)

The correct option is B.

Answer: The perimeter of a parallelogram is the sum of all its sides.

In this case, since all sides of the parallelogram WXYZ are given as 34 units, the perimeter of parallelogram WXYZ is the sum of all its four sides.

So the perimeter of parallelogram WXYZ = 34 + 34 + 34 + 34 = 136 units

It's important to notice that the given value of perimeter = 60 is not correct.

The perimeter of parallelogram WXYZ is 136 units, not 60 units.

Step-by-step explanation:

The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".

The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100

Simplifying the expression, we get:

5a + 10d = 100

Dividing both sides by 5, we get:

a + 2d = 20

Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:

1 + 2 * 1 = 3

Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.

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To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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1) Reject

2) Wrong

3) The given statement is not clear. The provided hypothesis format "H0: π(bbnk) π0" is incomplete and does not provide enough information to accurately interpret the fixed null hypothesis. Please provide a complete and clear hypothesis statement for a more accurate response.

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given 3(4h + 2k)

if this is expanded,

you have

12h + 6k

the option that is equivalent is the first one

which is

3(2k + 4h)

to expand,

6k + 12h

so the correct option is the first one wich is

3(2k + 4h)hello

are you th

Answer:

16

Step-by-step explanation:

The number after 15 s 16.

The solution to the initial value problem y' - 3y = 10e^(-t+4) sin²(2(t - 4)) - 44(t), with y(0) = 5, is y(t) = e^(3t) + 10e^(-t+4) sin(2(t - 4)) - 44t - 1.

To solve this problem, we'll start by finding the general solution to the homogeneous equation y' - 3y = 0. The characteristic equation is r - 3 = 0, which gives us the solution y₀(t) = Ce^(3t).

To solve the initial value problem y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t with y(0) = 5, we can use an integrating factor and the method of variation of parameters.

Step 1: Homogeneous Solution

First, let's find the homogeneous solution to the equation y' - 3y = 0. This means we solve the equation y' - 3y = 0 without the right-hand side term.

The characteristic equation is given by r - 3 = 0, which yields r = 3. Therefore, the homogeneous solution is y_h = C*e^(3t), where C is a constant.

Step 2: Particular Solution

Next, let's find a particular solution to the non-homogeneous equation y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t. We'll denote this particular solution as y_p.

For the term 10e^(-t), a suitable guess for the particular solution is y_p1 = A*e^(-t), where A is a constant to be determined.

Differentiating y_p1 with respect to t gives y_p1' = -A*e^(-t).

Substituting y_p1 and y_p1' into the differential equation, we have:

(-Ae^(-t)) - 3(Ae^(-t)) = 10e^(-t).

Simplifying, we get -4A*e^(-t) = 10e^(-t).

Comparing the coefficients on both sides, we find A = -10/4 = -5/2.

For the term 4sin(2(t - 4)), a suitable guess for the particular solution is y_p2 = Bsin(2(t - 4)) + Ccos(2(t - 4)), where B and C are constants to be determined.

Differentiating y_p2 with respect to t gives y_p2' = 2Bcos(2(t - 4)) - 2Csin(2(t - 4)).

Substituting y_p2 and y_p2' into the differential equation, we have:

(2Bcos(2(t - 4)) - 2Csin(2(t - 4))) - 3(Bsin(2(t - 4)) + Ccos(2(t - 4))) = 4sin(2(t - 4)).

Simplifying, we get (2B - 3C)cos(2(t - 4)) + (3B + 2C)sin(2(t - 4)) = 4sin(2(t - 4)).

Comparing the coefficients on both sides, we have the following system of equations:

2B - 3C = 0 (1)

3B + 2C = 4 (2)

Solving equations (1) and (2), we find B = 6/13 and C = 4/13.

For the term 44t, a suitable guess for the particular solution is y_p3 = Dt^2 + Et + F, where D, E, and F are constants to be determined.

Differentiating y_p3 with respect to t gives y_p3' = 2Dt + E.

Substituting y_p3 and y_p3' into the differential equation, we have:

(2Dt + E) - 3(Dt^2 + Et + F) = 44t.

Simplifying, we get -3Dt^2 + (2 - 3E)t + (E - 3F) = 44t.

Comparing the coefficients on both sides, we have the following system of equations:

-3D = 0 (3)

2 - 3E = 44 (4)

E - 3F = 0 (5)

Solving equations (3), (4), and (5), we find D = 0, E = -14/3, and F = -14/9.

Therefore, the particular solution is y_p = y_p1 + y_p2 + y_p3, which is:

y_p = (-5/2)e^(-t) + (6/13)sin(2(t - 4)) + (4/13)cos(2(t - 4)) - (14/3)t - (14/9).

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This equation gives V3 = 8.57 gallons, which is the volume of the final solution if you add 1 gallon of pure antifreeze

To find out how much pure antifreeze should be added to a 40% antifreeze solution to produce a solution that is 70% antifreeze, you can use the following equation:

V1 * C1 + V2 * C2 = V3 * C3

where "V1" is the volume of the initial solution, "C1" is the concentration of the initial solution, "V2" is the volume of the pure antifreeze being added, "C2" is the concentration of the pure antifreeze (which is 100%), "V3" is the volume of the final solution, and "C3" is the concentration of the final solution.

In this case, you are given that V1 = 5 gallons, C1 = 40%, C2 = 100%, and C3 = 70%. You want to find V2, the volume of pure antifreeze to be added.

Plugging these values into the equation gives:

(5 gallons) * (40%) + V2 * (100%) = (V3 gallons) * (70%)

Solving for V2, the volume of pure antifreeze to be added, gives:

V2 = (V3 * 70% - 5 gallons * 40%) / 100%

Since the volume of the final solution, V3, is not given, you cannot solve for V2 directly. However, you can solve for V3 in terms of V2 by rearranging the equation to solve for V3:

V3 = (V2 * 100% + 5 gallons * 40%) / 70%

Plugging in values for V2 and solving for V3 gives the volume of the final solution in terms of V2. For example, if you want to add 1 gallon of pure antifreeze, you can plug in V2 = 1 gallon and solve for V3:

V3 = (1 gallon * 100% + 5 gallons * 40%) / 70%

Solving this equation gives V3 = 8.57 gallons, which is the volume of the final solution if you add 1 gallon of pure antifreeze. You can repeat this process for different values of V2 to find the volume of the final solution for different amounts of pure antifreeze added.

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(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

What is Scatter Plot ?

A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.

In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.

One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.

Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.

Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

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Answer:

= 3/10 cm or you can put 0.3 cm