if you select three sticks, each of random length (between 0 and 1), what is the probability of being able to form a triangle with them?

Answer:

£3250

Step-by-step explanation:

ann : ben : cheryll

  3  :    7   :     10

The difference between ben and ann in the ratio is 7 - 3 = 4

The real difference between ben and ann is £650.

The real numbers are in the ratio 3:7:10, but they are many times greater than 3, 7, and 10.

Introduce a variable in the ratio.

3x : 7x : 10x

The difference between ben and ann is 7x - 3x = 4x.

The real difference between ben and ann is £650.

Therefore,

4x = £650

x = 162.5

The total money in the ratio is 3x + 7x + 10x = 20x

20x = 20(162.5) = 3250

Answer: £3250

Answer:

149,610 gallons

Step-by-step explanation:

To answer this question, we need to know the volume of Myron's swimming pool in cubic feet. Let's assume that the volume of Myron's swimming pool is 20,000 cubic feet.

Now we can use the given conversion factor to convert from cubic feet to gallons:

1 cubic foot = 7.48052 gallons

Therefore, the number of gallons of water needed to fill Myron's swimming pool is:

20,000 cubic feet x 7.48052 gallons/cubic foot = 149,610.4 gallons

So it will take approximately 149,610 gallons of water to fill Myron's swimming pool completely.

Answer: b 1:4

Step-by-step explanation:

Answer:

The given expression 15:60 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which is 15 in this case. So, 15 divided by 15 is 1 and 60 divided by 15 is 4. Therefore, the simplified form of 15:60 is 1:4. 

So, the answer is (b) 1:4.

The number of free throws expected basketball player to make by using proportion is equal to 180.

Percent of free throw attempted by basketball player = 80%

Number of free throws basketball player attempts in practice  = 225

If the basketball player makes 80% of the free throws she attempts,

we can expect her to make 80 out of every 100 free throws attempted.

To find out how many free throws she would make if she attempted 225, we can set up a proportion,

80/100 = x/225

We can solve for x by cross-multiplying the expression we get,

⇒ 100x = 80 × 225

⇒ 100x = 18000

⇒ x = 18000/100

⇒ x = 180

Therefore, we can expect the basketball player to make 180 free throws out of 225 attempts in practice using proportion.

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S is a function from the set of positive integers to the set of positive integers, defined as the sum of the positive divisors of a given integer. The questions to be answered are whether S is one-to-one, onto, or a one-to-one correspondence.

To determine if S is one-to-one, we need to check whether different inputs to the function produce different outputs. In other words, if S(a) = S(b) for some positive integers a and b, does it follow that a = b? To prove that S is not one-to-one, we can provide a counterexample. For example, S(6) = 1 + 2 + 3 + 6 = 12, and S(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56, but 6 ≠ 28. Therefore, S is not one-to-one.

To determine if S is onto, we need to check whether every positive integer is in the range of the function. In other words, for every positive integer y, is there some positive integer x such that S(x) = y? To prove that S is not onto, we can provide a counterexample. For example, there is no positive integer x such that S(x) = 2. Therefore, S is not onto.

A function is a one-to-one correspondence if it is both one-to-one and onto. Since S is not one-to-one and not onto, it is not a one-to-one correspondence.

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Answer:

1740 people

Step-by-step explanation:

A 16% increase is 0.16 as a decimal.

1500 * 0.16 = 240 more people expected next year

Add that 240 to the 1500 for the total number expected next year:

1500+240 = 1740 people

Answer: Approximately 1,740 people are expected to attend the homecoming football game this year, which is a 16% increase from last year's attendance of 1,500 people. This value is already rounded to the nearest person.

Step-by-step explanation:

Sure, let's calculate the expected attendance for this year's homecoming football game.

Step 1: Understand the problem

The problem states that there was an attendance of 1,500 people last year and this year there is expected to be a 16% increase in attendance. We need to find out the expected attendance for this year.

Step 2: Set up the equation

We can calculate the increase in attendance by multiplying last year's attendance by the percentage increase. The equation for this is:

New Attendance = Old Attendance + (Old Attendance * Percentage Increase)

Step 3: Substitute the given values into the equation

In this case, the Old Attendance is 1,500 and the Percentage Increase is 16% or 0.16 in decimal form. Substituting these values into the equation gives:

New Attendance = 1,500 + (1,500 * 0.16)

Step 4: Solve the equation

Let's calculate the result.

The calculation gives us:

New Attendance = 1,740

So, approximately 1,740 people are expected to attend the homecoming football game this year, which is a 16% increase from last year's attendance of 1,500 people. This value is already rounded to the nearest person.

Given that a ≡ b (mod n), it means that a and b have the same remainder when divided by n.

Step 1: Understand the notation a ≡ b (mod n). This notation means that when both a and b are divided by n, they have the same remainder.

Step 2: Apply the definition of modular arithmetic. If a ≡ b (mod n), there exists an integer k such that a = b + kn.

Step 3: Divide both sides of the equation by n. When you do this, you'll see that the remainder of a/n and b/n is the same, since the term kn is divisible by n and does not affect the remainder.

In conclusion, when a ≡ b (mod n), it means that both a and b have the same remainder when divided by n.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \implies {\large \begin{array}{llll} y +2 = 3 ( x -1) \end{array}}[/tex]

The critical value of F for a one-way between-subjects ANOVA with 4 and 43 degrees of freedom (5 levels minus 1, and 48 total participants minus 5 levels) at an alpha level of .01 is approximately 3.737.

To calculate the critical value of F, we need to use a statistical table or calculator. The F distribution table with 4 and 43 degrees of freedom at an alpha level of .01 gives a critical value of 3.737.

This means that if the calculated F value for the ANOVA is greater than 3.737, we can reject the null hypothesis at the .01 level of significance.

It's important to note that the critical value of F changes depending on the degrees of freedom and the alpha level chosen.

In this case, we have 5 levels/conditions and 48 participants, but if the sample size or number of levels changes, the critical value of F would be different.

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The null hypothesis for this test is that the mean weight of adult cats of the same breed is equal to 9.0 lb, while the alternative hypothesis is that it is different from 9.0 lb.

In statistical hypothesis testing, the null hypothesis is a statement that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis. In this case, the null hypothesis is that the mean weight of adult cats of the same breed is equal to 9.0 lb, which is what we are trying to test. The alternative hypothesis, on the other hand, is that the mean weight of adult cats of the same breed is different from 9.0 lb, which could be either higher or lower. This is the hypothesis that we would accept if there is sufficient evidence to reject the null hypothesis.

To test these hypotheses, we would need to collect a sample of adult cats of the same breed, measure their weights, and calculate the sample mean. We could then use statistical methods to determine whether the sample mean is significantly different from the hypothesized value of 9.0 lb. If it is, we would reject the null hypothesis in favor of the alternative hypothesis.

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The graph of the equation of the circle x² + (y - 3)² = 4² is drawn below.

Given that:

Equation, x² + y² - 6y = 7

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Convert the equation into a standard form, then we have

x² + y² - 6y = 7

x² + y² - 6y + 9 = 7 + 9

x² + (y - 3)² = 16

x² + (y - 3)² = 4²

The graph of the circle is drawn below.

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The inverse Laplace transform of 6s(s-8)^2 is f(t) = 3/4 - 9/16 e^(8t) + 3/32 t e^(8t). The inverse Laplace transform of each term separately,

To find the inverse Laplace transform of 6s(s-8)^2, we can use partial fraction decomposition to express the expression in terms of simpler Laplace transforms.

First, we factor the denominator of the expression to get:

6s(s-8)^2 = 6s(s-8)(s-8)

We can then use partial fraction decomposition to express this expression as:

6s(s-8)(s-8) = A/s + B/(s-8) + C/(s-8)^2

To solve for A, B, and C, we multiply both sides of the equation by the common denominator s(s-8)(s-8) and simplify to get:

6s = A(s-8)^2 + B(s)(s-8) + C(s-8)

Next, we substitute values of s that will make some of the terms vanish to solve for the coefficients A, B, and C.

Setting s = 0, we get:

0 = 64A - 8C

Setting s = 8, we get:

48 = 64A

Therefore, A = 3/4 and C = -3/32.

Substituting these values into the equation we obtained above, we get:

6s = 3/4(s-8)^2 + B(s)(s-8) - 3/32(s-8)

Simplifying, we get:

B = 9/16

Now we can express 6s(s-8)^2 in terms of simpler Laplace transforms:

6s(s-8)^2 = 3/4/s - 9/16/(s-8) - 3/32/(s-8)^2

Taking the inverse Laplace transform of each term separately, we get:

ℒ^-1 {3/4/s} = 3/4

ℒ^-1 {-9/16/(s-8)} = -9/16 e^(8t)

ℒ^-1 {-3/32/(s-8)^2} = 3/32 t e^(8t)

Therefore, the inverse Laplace transform of 6s(s-8)^2 is:

f(t) = 3/4 - 9/16 e^(8t) + 3/32 t e^(8t)

This is the solution to the problem.

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The three-month moving average of complaints for February, March, and April is 76, and this is predicted to be the number of complaints for May in the department store.

To use a three-month moving average to predict the number of complaints for May, we need to first calculate the average of the number of complaints for the three months leading up to May.

Here are the steps to do that:

Add up the number of complaints for the three months prior to May, which are February, March, and April:

48 + 86 + 94 = 228

Divide the sum by 3 to get the three-month moving average:

228 / 3 = 76

The predicted number of complaints for May is equal to the three-month moving average, which is 76. Therefore, using a three-month moving average, we predict that the number of complaints for May in the department store will be 76.

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Complete question:

How can we use a three-month moving average to predict the number of complaints for May, based on the table below which shows the number of complaints received in a department store for the first six months of operation?

Month Complaints

January 36

February 48

March 86

April 94

May         112

June 149

The length of the arc shown in red is 5π/4 metre

To find the length of the arc, we need to find the circumference of the circle, which we find with the following formula :

C = 2πr

where r  is the radius which is indicated in the image: .

so the circumference  is:

C = 2π(3)

C = 6π

This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.

Because we only want 30° of that 360 °, we divide the value of the circumference by 360 and multiply po 45:

30/360=0.125 of full circle,

L(arc)=0.125L=5π/4

The length of the arc is 5π/4 m

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The resulting displacement of the cyclist is approximately [tex]19.2[/tex] miles. (option C)

To find the resulting displacement of the cyclist, we can use the Pythagorean theorem since the cyclist traveled north and east, forming a right triangle.

The distance traveled north is 15 miles, and the distance traveled east is 12 miles. Let's call the northward distance "a" and the eastward distance "b."

Using the Pythagorean theorem, the resulting displacement "c" is given by:

[tex]\(c = \sqrt{a^2 + b^2}\)[/tex]

Plugging in the values, we have:

[tex]\(c = \sqrt{15^2 + 12^2}\)\\\c = \sqrt{225 + 144}\)\\\c = \sqrt{369}\)\(c \approx 19.2\) miles[/tex]

Therefore, the resulting displacement of the cyclist is approximately 19.2 miles.

So, the correct answer is option C: 19.2 miles.

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Answer:

 Diameter

Step-by-step explanation:

You have to draw the diameter and perpendicularly bisect it. Then, where the bisector touches the circumference, connect them (there should be 4 points of contact).

Hope this helps!

Answer:

$200

Step-by-step explanation:

To find the original price of an item that costs $217 with an 8.5% sales tax, you would first divide the total cost by 1 plus the tax rate (as the tax is calculated as a percentage of the original price plus tax). This would give you the price without the sales tax. So, $217 divided by 1.085 equals approximately $200. The original price before the sales tax was added would be $200.

The given statement is true. If x = f(t) and y = g(t) are twice differentiable, then d2y/dx2 = (d2y/dt2) / (d2x/dt2).

To prove the given statement, we will use the chain rule of differentiation. Let's start by differentiating x = f(t) with respect to t twice:

d/dt(x) = d/dt(f(t)) [Taking derivative of both sides]

dx/dt = df/dt

d2x/dt2 = d/dt(df/dt) [Taking derivative of the previous equation]

d2x/dt2 = d2f/dt2

Similarly, differentiating y = g(t) with respect to t twice:

d/dt(y) = d/dt(g(t)) [Taking derivative of both sides]

dy/dt = dg/dt

d2y/dt2 = d/dt(dg/dt) [Taking derivative of the previous equation]

d2y/dt2 = d2g/dt2

Now, using the chain rule, we can differentiate y with respect to x as follows:

dy/dx = dy/dt / dx/dt

dy/dx = (dg/dt) / (df/dt)

Differentiating the above equation with respect to x again, we get:

d2y/dx2 = d/dx[(dg/dt) / (df/dt)]

d2y/dx2 = d/dt[(dg/dt) / (df/dt)] * dt/dx [Using chain rule]

d2y/dx2 = [d/dt((dg/dt) / (df/dt))] / (d/dt(x)) [Using chain rule]

d2y/dx2 = [d2y/dt2 * df/dt - dy/dt * d2x/dt2] / (df/dt)^2 [Using quotient rule]

Substituting the values of d2y/dt2, d2x/dt2, and dy/dt from the earlier derivations, we get:

d2y/dx2 = (d2y/dt2) / (d2x/dt2)

Hence, the given statement is true.

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The balance of the account after 7 years would be approximately $247.95.

We may use the compound interest calculation to determine the account balance after seven years:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the final amount (balance) in the account

P = the principal amount (initial deposit)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, P = $150, r = 7.4% = 0.074 (as a decimal), n = 4 (quarterly compounding), and t = 7.

Plugging in these values into the formula, we get:

[tex]A = 150(1 + 0.074/4)^{(4\times7)[/tex]

Calculating this expression, we find:

A ≈ $247.95

Therefore, the balance of the account after 7 years would be approximately $247.95.

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The perimeter of triangle ABC is approximately 24.53 units.

To find the perimeter of triangle ABC, we need to know the lengths of all three sides. We can use the given information about the angles and side lengths to solve for the missing side lengths using trigonometry.

Let's start with the side opposite the 29-degree angle, which we'll call side AB. We can use the sine function to find the length of AB:

sin(29) = opposite/hypotenuse

opposite = sin(29) x 10

opposite ≈ 4.83

So, side AB has a length of approximately 4.83 units.

Next, let's move on to the side opposite the 61-degree angle, which we'll call side AC. We can use the same process:

sin(61) = opposite/hypotenuse

opposite = sin(61) x 10

opposite ≈ 8.66

So, side AC has a length of approximately 8.66 units.

Finally, we know that one of the angles in the triangle is 90 degrees, so the third angle must be:

180 - 90 - 29 = 61 degrees

This means that side BC is the hypotenuse of a right triangle with one leg of length 4.83 and the other leg of length 8.66. We can use the Pythagorean theorem to find the length of BC:

BC² = AB² + AC²

BC² = 4.83² + 8.66²

BC² ≈ 94.08

BC ≈ 9.7

So, side BC has a length of approximately 9.7 units.

Now that we have the lengths of all three sides, we can find the perimeter of triangle ABC:

Perimeter = AB + BC + AC

Perimeter = 4.83 + 9.7 + 10

Perimeter ≈ 24.53

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Answer:

4 pizzas

Step-by-step explanation:

first of all, subtract parking fee from total:

52 - 4 = 48.

now divide by 12:

48/12

4.

so he he pays for 4 pizzas at $12 each (4 X 12 = 48).

and he pays $4 for parking.

48 + 4 = 52.

The height of the trapezoid is 14 units.

We need to find the height of a trapezoid which has given lengths of its bases and the area.

Area = (1/2) × (sum of the bases)×height

The area is given as 518, and the lengths of the bases are 30 and 44.

Plug in these values.

518 = (1/2) × (30 + 44) × height

518 = (1/2) × 74 × height

Now, let's solve for the height:

518 = 37 × height

Divide both sides by 37:

height = 518 / 37

height = 14

Therefore, the height of the trapezoid is approximately 14 units.

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Answer:

C

Step-by-step explanation:

To represent the system of equations step by step using matrices, we'll start by setting up the coefficient matrix and the constant matrix. Let's go through the process:

Step 1: Write down the equations:

Equation 1: y = 10

Equation 2: 4x - 5y = 3

Step 2: Set up the coefficient matrix (matrix A):

Coefficients of Equation 2: 4 and -5

Coefficients of Equation 1: 0 and 1

A =

| 4 -5 |

| 0 1 |

Step 3: Set up the constant matrix (matrix B):

Constants of Equation 2: 3

Constants of Equation 1: 10

B =

| 3 |

| 10 |

Step 4: Combine the coefficient matrix and constant matrix into an augmented matrix (matrix [A|B]):

[A|B] =

| 4 -5 3 |

| 0 1 10 |

This augmented matrix represents the system of equations:

4x - 5y = 3

0x + 1y = 10

Each row in the augmented matrix corresponds to an equation in the system. The first column represents the coefficients of x, the second column represents the coefficients of y, and the last column represents the constants.

Therefore, the matrix that represents the system of equations is:

C.

0 1 3

4 -5 10

We would need a sample size of approximately 598 men to have a 90% chance of detecting a true proportion of 8% with a significance level of 0.1.

To determine the sample size required, we need to perform a hypothesis test. The null hypothesis is that the proportion of men playing golf is 5%, and the alternative hypothesis is that it is greater than 5%.

We want to have a significance level (alpha) of 0.1, which corresponds to a confidence level of 0.9, and we also want a statistical power of 0.9. Assuming a one-tailed test, we can use a z-test to calculate the sample size needed.

Using a statistical calculator, we find that the critical value of z for a significance level of 0.1 is 1.28, and the critical value of z for a power of 0.9 is 1.28 + 1.28 = 2.56. The effect size is 0.03, which is the difference between the hypothesized proportion of 0.05 and the true proportion of 0.08. Plugging these values into the sample size formula for a z-test, we get:

n = ((1.28 + 2.56) / 0.03)² = 597.3

Therefore, we would need a sample size of approximately 598 men to have a 90% chance of detecting a true proportion of 8% with a significance level of 0.1.

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There are 35 possible combinations of 3 employees that can be chosen from the set of 7 at Dunder Mifflin Paper Company.

To find the number of combinations of 3 employees that can be chosen from the set of 7, we can use the formula for combinations:

nCr = n! / (r! * (n-r)!)

where n is the total number of employees (7 in this case) and r is the number of employees we want to choose (3 in this case).

Plugging in the values, we get:

7C₃ = 7! / (3! * (7-3)!)

= (7 * 6 * 5) / (3 * 2 * 1)

= 35

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The value of the diameter of the base of the cylinder is,

⇒ d = 8

We have to given that;

The volume of a cylinder is 96 π cubic meters

And, the height is 6 meters.

Since, We know that;

Volume of cylinder is,

V = πr²h

Substitute all the values we get;

96π = π × r² × 6

16 = r²

r = √16

r = 4

Thus, The value of the diameter of the base of the cylinder is,

⇒ d = 4 × 2

⇒ d = 8

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Answer: No it is a quadratic function

Step-by-step explanation: the solution to this would be

y=(3-x)4x

y=-4x^2+12x

which would make it a parabola, which is quadratic function

The scale factor used to create the image is given as follows:

k = 1.5.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The length of segment AB is given as follows:

AB = -6 - (-14) = 14 - 6 = 8.

The length of segment A'B' is given as follows:

A'B' = -9 - (-21) = 21 - 9 =12.

Hence the scale factor is given as follows:

k = 12/8

k = 1.5.

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Answer:

1.5

Step-by-step explanation:

The first question requires finding the roots of a quadratic equation using factorization, the second question requires finding the derivative of a given function with respect to x, the third question requires calculating compound interest for a given period, and the fourth question requires finding the sum of the first 70 terms of an arithmetic progression.

To solve the quadratic equation x² + 3x - 28 = 0 using factorization, we need to find two numbers whose sum is 3 and whose product is -28. The two numbers are 7 and -4. Therefore, we can write the quadratic equation as (x + 7)(x - 4) = 0, which gives the roots x = -7 and x = 4.

To find the derivative of 2-2ut4 with respect to x, we need to treat t as a constant and apply the power rule of differentiation. The derivative is -8ut3(d/dx)(2-2ux) = -8ut3(-4u) = 32u2t3.

To find the compound interest for 3 years at 8,000.00 with an annual interest rate of 10%, we can use the formula A = P(1 + r/n)nt, where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, P = 8,000.00, r = 10%, n = 1 (since interest is compounded annually), and t = 3. Plugging in these values, we get A = 8,000.00(1 + 0.10/1)1(3) = 10,480.00. Therefore, the compound interest for 3 years is 2,480.00.

To find the sum of the first 70 terms of an arithmetic progression whose 10th and 12th terms are 50 and 65, respectively, we need to first find the common difference (d) and the first term (a1). Using the formula for the nth term of an arithmetic progression, we can write the equations a10 = a1 + 9d = 50 and a12 = a1 + 11d = 65. Solving these equations simultaneously, we get a1 = 22 and d = 3. Therefore, the sum of the first 70 terms is given by the formula S70 = (n/2)(2a1 + (n-1)d), where n = 70. Plugging in the values, we get S70 = (70/2)(2(22) + (70-1)3) = 3,955.

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