1) The rational function shown could be used to the number of arrests, f(x), per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver’s age, x.

\(f(x)=\frac{27725(x-14)}{x^2+9} -5x\)

a) Describe the trend you see in the graph, in context.
b)Use a graphing utility to determine the age that corresponds to the greatest number of arrests.

Answer:

Aprox: 1.61

Step-by-step explanation:

TOA: Tan Q = Opposite/Adjacent = 45/28 ---> 1.61

Answer:

28/45≈1.6071≈1.61

Step-by-step explanation:

The solution is the factor 4y - 6x:. 2(2y - 3x) = 2(2y - 3x). 8 = 2• 4 =. 2(2y - 3x)

8. 2• 4

cancel the common factor: 2

= 2y - 3x. the answer is 2y - 3x

4 4

Answer:

Its -15 or D

Step-by-step explanation:

Answer:

D. -15

Step-by-step explanation:

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

The pool can contain 10492 gallons of water

What is volume of cylinder?

The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

Right circular cylinder: A cylinder with circular bases and a lateral curved surface with each line segment perpendicular to the bases.

Oblique Cylinder: A cylinder with sides that are inclined over the base at a different angle than a right angle.

An elliptic cylinder is a cylinder with ellipses at its bases.

Two right circular cylinders tied together inside of one another form a right circular hollow cylinder.

volume of cylinder= (π)\(r^2h\)

diameter= 18feet

radius = 9 feet

height = 5.5 feet

volume= 3.14*(\(9^2\))*5.5

     = 1398.87 \(feet^3\)

volume in gallons = 1398.87 * 7.5

                 = 10492 gallons

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So, there are (n!)^2 ways to arrange n men and n women in a row if they alternate genders.

We need to use the principle of multiplication. We first choose the position of the first person in the row, which can be any of the n men or n women. Without loss of generality, let's say we choose a man. Then, for the next position, we need to choose a woman since we are alternating genders. There are n women to choose from. For the third position, we need to choose another man, and there are n-1 men left to choose from (since we already used one). For the fourth position, we need to choose another woman, and there are n-1 women left to choose from. We continue this pattern until all n men and n women are placed in the row.

Using the principle of multiplication, we can find the total number of ways to arrange the people by multiplying the number of choices at each step. Therefore, the total number of ways to arrange the people in a row if the men and women alternate is:

n * n-1 * n * n-1 * ... * 2 * 1

This can be simplified to:

(n!)^2

So, there are (n!)^2 ways to arrange n men and n women in a row if they alternate genders.

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Answer: Angle T is 45

Step-by-step explanation:

Answer:

\(g^{-1}(x)=1+10^{x/2}\)

Step-by-step explanation:

Inverse Function

Let's call:

\(y=2 log(x-1)\)

Divide by 2:

\(y/2=log(x-1)\)

Assuming the base of the log is 10, apply exponential base 10:

\(10^{y/2}=x-1\)

Solving for x:

\(x=1+10^{y/2}\)

Swap variables:

\(y=1+10^{x/2}\)

Calling this function the inverse:

\(\boxed{g^{-1}(x)=1+10^{x/2}}\)

The registrants would be able to see the 6 sightseeing tours in 18 ways.

Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.

This implies that the 6 sightseeing tours are available on all three days.

Hence, the registrants would be able to book the tour on any of the one days.

Hence, on day 1

the registrants will be able to tour in  ways

On day 2

the registrants would again be able to tour in 6 ways,

Similarly on day 3, they will again be able to tour in 6 ways.

Since they need to choose either of the days given, the total number of ways to tour will be

no.of ways for day 1  +  no. of ways for day 2  +  no. of d6ays for day 3

= 6  +  6  +  6

= 18 ways

Hence, they can go on a sightseeing tour in 18 ways.

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when u = 2,v = 1, and w = 0, the partial derivatives are

∂u/∂z = 0,

∂v/∂z = 0, and

∂w/∂z = 0.

To find the partial derivatives ∂u/∂z, ∂v/∂z, and ∂w/∂z using the Chain Rule, we follow these steps:

Calculate ∂u/∂z:

∂u/∂x = 0 (since u is a constant)

∂u/∂y = 0 (since u is a constant)

∂x/∂z = y² (using the given expression for z)

∂y/∂z = 0 (since y is not directly dependent on z)

Plugging these values into the formula:

∂u/∂z = (∂u/∂x) * (∂x/∂z) + (∂u/∂y) * (∂y/∂z)

= 0 * y² + 0 * 0

= 0.

Calculate ∂v/∂z:

∂v/∂x = 0 (since v is a constant)

∂v/∂y = 0 (since v is a constant)

∂x/∂z = y² (using the given expression for z)

∂y/∂z = 0 (since y is not directly dependent on z)

Plugging these values into the formula:

∂v/∂z = (∂v/∂x) * (∂x/∂z) + (∂v/∂y) * (∂y/∂z)

= 0 * y² + 0 * 0

= 0.

Calculate ∂w/∂z:

∂w/∂x = 0 (since w is a constant)

∂w/∂y = 0 (since w is a constant)

∂x/∂z = y² (using the given expression for z)

∂y/∂z = 0 (since y is not directly dependent on z)

Plugging these values into the formula:

∂w/∂z = (∂w/∂x) * (∂x/∂z) + (∂w/∂y) * (∂y/∂z)

= 0 * y² + 0 * 0

= 0.

Therefore, When u = 2, v = 1, and w = 0, the partial derivatives ∂u/∂z,

∂v/∂z, and ∂w/∂z are all equal to 0.

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Answer:

Acute angle

Step-by-step explanation:

Since it's measure is less than 90 degrees

Answer:

Let one integer be x, and the other be (x+2)

x(x+2)=224

x2+2x-224=0

(x+16)(x-14) =0

x=-16 or 14

so x+2 = -14 or 16

So the integers are either 14 and 16 or -14 and -16.

Step-by-step explanation:

was that the question?

Let the first consecutive even number be x. The second one is going to be two more than x, and as such can be written as (x+2).

The product of these numbers, x and (x+2), is 224:

x(x+2)=224

x²+2x=224

x²+2x-224=0

(x+16)(x-14) =0 (could also use '-b' method)

x=-16 or 14

Therefore, (x+2) = -14 or 16

Therefore, the numbers are either 14 and 16, or -14 and -16

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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The value of x is 4.47 units

In the given figure, there are two right angle triangle, to find the value of x we have to solve each triangle using the Pythagorean theorem.

Consider the bottom triangle

Base of the triangle = 6 units

The hypotenuse of the triangle = 9 units

Apply the Pythagorean theorem

The third side of the triangle = \(\sqrt{9^2-6^2}\)

= \(\sqrt{81-36}\)

= \(\sqrt{45}\) units

Similarly consider the top triangle

The base of the triangle = 5 units

The hypotenuse of the triangle = \(\sqrt{45}\) units

The third side of the triangle = \(\sqrt{\sqrt{45}^2- 5^2}\)

= \(\sqrt{45-25}\)

= \(\sqrt{20}\)

= 4.47 units

Hence, the value of x is 4.47 units

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Therefore, the average height of the particle on the interval [-1, 5] is approximately 33.67 feet.

To find the average height of the particle on the interval [-1, 5], we need to evaluate the definite integral of the position function f(x) = 3x^2 + 6x over that interval and divide it by the length of the interval.

The average height (H_avg) is calculated as follows:

H_avg = (1 / (b - a)) * ∫[a to b] f(x) dx

In this case, a = -1 and b = 5, so the average height is:

H_avg = (1 / (5 - (-1))) * ∫[-1 to 5] (3x^2 + 6x) dx

To evaluate the integral, we can use the power rule of integration:

∫ x^n dx = (1 / (n + 1)) * x^(n+1) + C

Applying this rule to each term in the integrand, we get:

H_avg = (1 / 6) * [x^3 + 3x^2] evaluated from -1 to 5

Now, we can substitute the limits of integration into the expression:

H_avg = (1 / 6) * [(5^3 + 3(5^2)) - ((-1)^3 + 3((-1)^2))]

H_avg = (1 / 6) * [(125 + 75) - (-1 + 3)]

H_avg = (1 / 6) * [200 - (-2)]

H_avg = (1 / 6) * 202

H_avg = 33.67 feet

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Answer:

Table 2.

Step-by-step explanation:

Recall that by definition, a linear function increases linearly. That is, the rate of change between any two points is constant.

We can go through each table and verify its rate of change.

Table 1)

For Table 1, note that y = -19 when x = 0.

When x = 1, y = -11. In other words, we added 8 for every increase of one for x.

When x = 2, y = -3. We still increased by 8 for every increase of one for x.

When x = 3, y = 5. Since -3 + 8 = 5, all points in Table 1 shows a constant rate of change.

In conclusion, Table 1 represents a linear function.

Table 2)

For Table 2, note that y = -1.5 when x = 0.

When x = 1, y = -1.5. In other words, we increased by 3 for every increase of one for x.

However, when x = 2, y = 3. This time, we only increased by 1.5 for every increase of one for x. Since the two rates are not equivalent, Table 2 is nonlinear.

Table 3)

Again, note that for Table 3, y = 15 when x = 0.

When x = 1, y = 12. So, we decreased by 3 for every increase of one for x.

When x = 2, y = 9. And when x = 3, y = 6. For both cases, we still decreased by 3 for every increase of one for x.

In conclusion, Table 3 represents a linear function.

Therefore, the table that represents a nonlinear function is Table 2.

Answer:

Step-by-step explanation:

product of (2.5 x 10²) x (10⁵)=2.5 x 10⁷

when we multiply the powers we add the 2+5=7

Answer:

9.25×10^7

Step-by-step explanation:

2.5 × 3.7 =9.25 and 10^2+10^5=10^7

Answer:

180°

Step-by-step explanation:

The baseball game lasted 2 hours and 10 minutes.

To calculate how long the baseball game lasted, we must begin by taking the start time of 7:05. We can convert this time to a numerical value by adding 7 hours and 5 minutes, which equals 705 minutes. Next, we must do the same with the end time of 9:15. Adding 9 hours and 15 minutes gives us a total of 915 minutes. Subtracting the start time from the end time gives us a difference of 210 minutes. Finally, we must convert the minutes back to hours and minutes, which gives us 2 hours and 10 minutes. Therefore, the baseball game lasted 2 hours and 10 minutes.

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Answer:

7664025600

Step-by-step explanation:

I basically just multiplied first then added the sums. Also you can use a calculator to make sure ur answer is right.

Answer:

g(1) = 72

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define

g(x) = 9(2x² + 6)

g(1) is x = 1

Step 2: Solve

Answer:

a) The equation of the parabola

                        \(y = \frac{-x^{2} }{4} +5\)

Step-by-step explanation:

Explanation:-

Step(i):-

Given the directrix of the parabola y = 6

Focus of the parabola S(0,4)

The standard equation of the parabola

                  ( x- h)² = 4 a (y-k)

(h,k) is the vertex of the parabola

Axis of the parabola is parallel to y-axis

Given the directrix of the parabola y = 6

The directrix of the parabola y = k -a = 6

                                k-a =6 ...(i)

The focus of the parabola

                         S( h , K+a) = (0,4)

so   h = 0 and K+a =4

                          K+a =4 ....(ii)

Step(ii):-

Solving (i) and (ii) equations , we get

    Adding (i) and (ii) equations and we get

     K-a + k+a = 6 +4

               2 K = 10

                  K =5

Substitute   K =5 in equation (i)

             K -a =6

            5 -a =6

            5-6 =a

            a = -1

Step(iii):-

we have (h,k) =( 0,5)  and a = -1

The equation of the  parabola

                                 ( x- h)² = 4 a (y-k)

                                 ( x- 0)² = 4 (-1) (y-5)

                                x²  = -4 y + 20

                              -4 y =   x²  - 20

dividing '-4' on both sides, we get

                         \(y = \frac{x^{2} }{-4} +\frac{-20}{-4}\)

                          \(y = \frac{-x^{2} }{4} +5\)

Final answer:-

The equation of the parabola

                        \(y = \frac{-x^{2} }{4} +5\)

The given statement "Under random sampling from an infinite population, the mean of the sampling distribution of the sample mean is always equal to the mean of the underlying population" is TRUE.

The reason for this is that the central limit theorem (CLT) applies to large enough random samples from any population with a finite variance. According to CLT, the sampling distribution of the mean becomes approximately normal, and its mean is equal to the mean of the population.

Since the statement specifies an infinite population, it is not technically possible to obtain a sample size large enough to meet the requirements of CLT.

However, the statement remains true in theory because an infinite population with a finite variance can be thought of as a limit of a sequence of finite populations, each of which does meet the requirements of CLT.

Therefore, even though it is not practically possible to obtain a truly random sample from an infinite population, the statement remains true in theory.

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Answer:

75°, 85°, 95°, 105°

Step-by-step explanation:

Since the 4 angles form an AP, then the 4 angles are

a, a + d, a + 2d, a + 3d

where a is the first term and d the common difference

The sum of the angles in a quadrilateral = 360° thus

a + a + d + a + 2d + a + 3d = 360, that is

4a + 6d = 360, substitute d = 10

4a + 60 = 360 ( subtract 60 from both sides )

4a = 300 ( divide both sides by 4 )

a = 75

Thus the 4 angles are

75°, 75° + 10° = 85°, 75° + 20 = 95°, 75° + 30° = 105°

Answer:

(-12x^9+3x^7+24x^6)÷6=-2×^10+1/2x^8+4x^7

32 x 134

Partial product: Multiply each digit of 32 by each digit of 134, maintain each digit place.

(30x100) + (30x 30) + (30 x4)+ (2 x 100) + (2x30) + (2 x 4)

3,000 + 900+120+200+60+8 = 4,288

Answer:

The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.

Step-by-step explanation:

To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:

s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)

= (96 +/- sqrt(9216 + 4352)) / -32

= (96 +/- sqrt(13,568)) / -32

Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:

s = (96 + sqrt(13,568)) / -32

= (96 + 120) / -32

= 0.5625 seconds

Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.

To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.

Answer:

\( {(x + y)}^{2} - 1\)

Step-by-step explanation:

\( {x}^{2} + y(y - 2x) - 1\)

\( {x}^{2} + {y}^{2} - 2xy - 1\)

Using the identity (a - b)^2 here ,

\( {(x + y)}^{2} - 1\)