The padlock for your gym locker uses a 3 number sequence to open the lock. If the numbers go from 1 to 27, how many different sequences are there on the dial without repeating a number?A. 17,550B. 33,696C. 16,848D. 8,775

Answer:

1/5

Step-by-step explanation:

Refer to the image for the region. I've chosen to "scan" the region horizontally for convenience sake, so x varies for values between the green and the red line, and y varies from 0 to 1.

The two lines have equations \(x=7-6y\) (red line) and \(x=7-7y\) (green line). Since we're integrating first with respect to x, it's easier to write the equation like that and not as \(y=mx+q\) since they will become our new limits of integration

Our double integral will become

\(\int \limits_0^1 \ \ \int \limits_{7-7y}^{7-6y}y^3dxdy = \int \limits_0^1 y^3x|\limits_{7-7y}^{7-6y} dy =\\\int \limits_0^1 y^3[(7-6y)-(7-7y)]dy = \int \limits_0^1y^3(y)dy =\\\int \limits_0^1 y^4dy =\frac15y^5|\limits_0^1=\frac15\)

The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

S = 7cm

Step-by-step explanation:

A = 49cm² = 7 × 7 (Square root of 49 as Area = s²)

S = 7cm

The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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The condition probability of a given b must be smaller than the intersection of the same two events a and b:

This statement is False.

The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".

The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.

The formula for conditional probability is

where P(b|a) represents the probability of event "b" given that event "a" has already occurred.

In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".

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The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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The inverse function of the given function is f⁻¹(x) = 10, 6, 5, 4.

What is inverse function ?

An inverse function is a function that "undoes" the effect of another function. More specifically, if a function f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes the output y and produces the input x that was used to generate it.

To find the inverse of a function, we need to follow these steps:

Replace the function notation with "y".

Swap the x and y variables.

Solve for y in terms of x.

Replace y with f⁻¹(x) to write the inverse function in function notation.

Let's apply these steps to the given function:

x = 5, 8, 9, 13

y = 10, 6, 5, 4

Replace the function notation with "y":

y = 10, 6, 5, 4

Swap the x and y variables:

x = 10, 6, 5, 4

Solve for y in terms of x:

To solve for y, we need to isolate it on one side of the equation:

y = f⁻¹(x)

Replace y with f⁻¹ (x) to write the inverse function in function notation:

f⁻¹(x) = 10, 6, 5, 4

Therefore, the inverse function of the given function is f⁻¹(x) = 10, 6, 5, 4.

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Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Answer:

Step-by-step explanation:

If 11 flights were sampled with an 85% on-time arrival rate, the number of flights from the sample that arrived on time would be estimated to be 9.35, which would round to 9 flights.

This can be solved by:

(0.85x11)= 9.35

Since there can't be .35 of a flight, we would round to the nearest whole number, which would just be 9.

The final answer= 9 flights

1. The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are 49.

4. The number of students like Foreign in a class of 225 are 18.

5. The number of students like Horror in a class of 200 are 22.

6. The number of students like Science friction in a class of 175 are 14.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The pie chart is,

Comedy   27%

Action       18%

Romance  14%

Drama      14%

Horror      11%

Foreign    8%

Science    8%

Now,

1. The number of students like Comedy in a class of 300 are;

= 27% of 300

= 27/100 x 300

= 81

Thus, The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are;

= 18% of 400

= 18/100 x 400

= 72

Thus, The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are;

= 14% of 350

= 14/100 x 350

= 49

4. The number of students like Foreign in a class of 225 are;

= 8% of 225

= 8/100 x 225

= 18

5. The number of students like Horror in a class of 200 are;

= 11% of 200

= 11/100 x 200

= 22

6. The number of students like Science friction in a class of 175 are;

= 8% of 175

= 8/100 x 175

= 14

Thus, 1. The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are 49.

4. The number of students like Foreign in a class of 225 are 18.

5. The number of students like Horror in a class of 200 are 22.

6. The number of students like Science friction in a class of 175 are 14.

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Answer:

w=4, y= 4sqrt2

Step-by-step explanation:

45 45 90 triangle property

Answer:

9+3t

Step-by-step explanation:

Let the variable be x

A number isn’t given so pick any number.

Let’s use 10

Set up the equation to get:

X + 10 = -8

Solve for the variable by subtracting 10 from both sides:

X = -18

Let the variable be y and pick any number, let’s use the number 2.

Equation: 2 x y = 4/5

Solve for y by dividing both sides by 2:

Y = 2/5

Answer:

14 cups = 7 pints

144 cups = 36 quarts

Step-by-step explanation:

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

The answer will be -45/4 or -11 1/4

Step-by-step explanation:

The first thing you will do is convert both numbers into improper fractions. -4 1/2 will be -9/2 and 2 1/2 will be 5/2. Once you do that, you will multiply each fraction and you should get -45/4. Finally, you would convert that into a mixed number which would be -11 1/4.

Hope that helps and if not, let me know!!

The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

Given are two right triangles we need to find the missing sides,

We will use Trigonometric ratios to find the same.

We know that,

Sin a = perpendicular / hypotenuse

Cos a = base / hypotenuse

Tan a = perpendicular / base

1) Sin 60° = x / 4√3

x = √3/2 × 4√3

x = 6

Cos 60° = y / 4√3

1/2 × 4√3 = y

y = 2√3

2) Cos 60° = x / 98

x = 1/2 × 98

x = 49

Sin 60° = y / 98

√3/2 = y / 98

y = 49√3

Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

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To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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The angle  made by one of the tensions suspending particle P is 50⁰.

The angle θ made by one of the tensions is calculated by applying trig identities as follows;

the force opposite the angle = weight of the block = mg

W = 7.75 kg x 9.8 m/s²

W = 75.95 N

The angle θ made by one of the tensions is calculated as follows;

cos θ = (38 N ) / ( 59 N)

cos θ = 0.6441

θ = arc cos (0.6441)

θ = 50⁰

Thus, the angle θ made by one of the tensions is determined as 50 degrees.

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The missing part of the question is in the image attached.

Answer:

The equation that represents the situation is: 30w = 150.

Step-by-step explanation:

We can set up an equation to find the value of w:

30w = 150

To solve for w, we can divide both sides of the equation by 30:

w = 150 / 30

w = 5

So April walks dogs for 5 weeks to earn $150.

Answer:

22 weeks

Step-by-step explanation:

it is 22 weeks because if you divide 39 by 2 then it is 19.5 and if you divide 429 by 19.5 you will get 22 hope this helps.

The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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The correct pattern and next three terms in the sequence -15, -11, -7, -3, is,

d. Add 4; 1, 5, 9

We have to given that,

The sequence is,

⇒ - 15, - 11, - 7, - 3, ...

Now, We have to see that,

⇒ - 15 + 4 = - 11

⇒ - 11 + 4 = - 7

⇒ - 7 + 4 = - 3

Hence, The rule is add 4 in first term to find next terms.

So, The next three terms are,

⇒ - 3 + 4 = 1

⇒ 1 + 4 = 5

⇒ 5 + 4 = 9

Thus, The correct pattern and next three terms in the sequence -15, -11, -7, -3, is,

d. Add 4; 1, 5, 9

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Answer:

Quick Stop -

3 apples = $1.29

1 apple = $0.43

Shop -

5 apples = 2.45

1 apple = 0.49

So the quick stop is better!

Answer:

2(8-d)

Step-by-step explanation:

16 - 2d

Answer:

2 x (8 - d)

Step-by-step explanation:

2 times means multiply by 2

difference of 8 and d means 8 minus d → 8 - d

Answer:

3

Step-by-step explanation:

Answer: c 5 cm

Step-by-step explanation: 40 - 35 is 5 cm

The volume of the rock will be 10 cm³.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The initial volume = 20 ml

And, The final volume = 30 ml

Now,

Since, The initial volume = 20 ml

And, The final volume = 30 ml

Hence, The volume of rock = 30 ml - 20 ml

                                          = 10 ml

Here, 1 ml = 1 cm³

Thus,  The volume of rock = 10 cm³.

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The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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