1. A report from the Secretary of Health and Human Services stated that 70% of single-vehicle traffic fatalities that occur at night on weekends involve an intoxicated driver. If a sample of 15 single-vehicle fatalities that occur on a weekend night is selected, find the probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated. (7 points)

Two lines intersect at a 54 degree angle.

Note that the composition of reflections over two intersecting lines is equivalent to a rotation, which is two times the angle measure at the point of rotation.

Therefore, the measure of the resulting rotation is

54 x 2 = 108.

The measure of the resulting rotation is 108 degrees.

Answer:

Given: ratio of boy to girl campers

8:7

8+7=15

195÷15=13

8×13 = number of boy campers

= 104 boys

so there are 104 boy campers

and if you were to work out the girls, you do 7 multiplied by 13, which is 91

Answer:

Step-by-step explanation:

Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.

Thus, the cardinal number of the set E is found to be: N(E) = 6.

A cardinal number describes or expresses how many of anything are present.

So all natural numbers are often refereed to as cardinal numbers. Cardinal numerals have been used for counting. When an ordinal number is an integer that represents the location or place of an object.

The description of a cardinal number is really a number that is used to express quantity in whole numbers. Decimals and fractions are not regarded as cardinal numbers. Natural numbers and numbering numbers constitute cardinal numbers. Each of them is a positive integer.

Given data:

N(CxE) = 18

C = {4, 5, 6)

In which N is the cardinal number, that is the total elements present in the set.

So,

N(C) = 3

Given that: N(CxE) = 18

The formula for the Cartesian product is:

N(CxE) = N(C) * N(E)

18 = 3* N(E)

N(E)  = 18 /3

N(E) = 6

Thus, the cardinal number of the set E is found to be: N(E) = 6.

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Complete questions:

Find N(E), Given That N(CxE) = 18 And C = {4, 5, 6).

Α. 6

B. 9

C. 3

D. 5

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2

Answer:

0.4

Step-by-step explanation:

Answer:

\(Ratio = 11:13\)

Step-by-step explanation:

Represent Amar age with x

Represent Kabir age with y

So, we have:

Presently

\(x : y = 3 : 4\)

After 4 years

\(x + 4 : y + 4 = 7 : 9\)

Simplify both ratios:

\(x : y = 3 : 4\)

\(\frac{x}{y} = \frac{3}{4}\)

Cross Multiply

\(4x = 3y\)

Make x the subject

\(x = \frac{3}{4}y\)

\(x + 4 : y + 4 = 7 : 9\)

\(\frac{x + 4}{y + 4} = \frac{7}{9}\)

Cross Multiply

\(7(y+4) = 9(x+4)\)

Open Brackets

\(7y + 28 = 9x + 36\)

Collect Like Terms

\(9x = 7y + 28 - 36\)

\(9x = 7y -8\)

Substitute \(\frac{3}{4}y\) for x in \(9x = 7y -8\)

\(9(\frac{3}{4}y) = 7y - 8\)

\(\frac{27}{4}y = 7y - 8\)

\(6.75y = 7y - 8\)

\(6.75y - 7y = - 8\)

\(-0.25y = - 8\)

\(y = -8/-0.25\)

\(y = 32\)

Substitute 32 for y in \(x = \frac{3}{4}y\)

\(x = \frac{3}{4} * 32\)

\(x = \frac{3* 32}{4}\)

\(x = \frac{96}{4}\)

\(x = 24\)

So, in 20 years time, the ratio of the ages would be:

\(x + 20 : y + 20\)

This gives

\(24 + 20 : 32 + 20\)

\(44 : 52\)

Divide by 4

\(44/4:52/4\)

\(11:13\)

Hence, the Ratio is

\(Ratio = 11:13\)

Answer:

0.43

Step-by-step explanation:

x = sin^-1(0.4)

x = 23.57

tan(23.57) = 0.436

a) The radius of the original large cone is approximately 9.4 m.

b) The volume of the frustum is approximately 617 m^3.

a) To calculate the radius of the original large cone, we can use the concept of similar triangles. In the given diagram, we have a frustum formed by removing a smaller cone from a larger cone.

The height of the frustum is 3 m, the radius of the larger base (R1) is 10 m, and the radius of the smaller base (R2) is unknown. The height of the larger cone (H) is 50 m.

Using the similar triangles formed by the frustum and the larger cone, we can set up the following proportion:

(R1 - R2) / h = R1 / H,

where h is the height of the frustum.

Substituting the known values, we have:

(10 - R2) / 3 = 10 / 50.

Simplifying the equation, we find:

(10 - R2) / 3 = 1/5.

Cross-multiplying and solving for R2, we get:

50 - 5R2 = 3,

5R2 = 47,

R2 ≈ 9.4 m.

b) To calculate the volume of the frustum, we can use the formula for the volume of a frustum of a cone:

V = (1/3) * π * h * (R1^2 + R2^2 + R1 * R2).

Substituting the known values, we have:

V = (1/3) * π * 3 * (10^2 + 9.4^2 + 10 * 9.4).

Evaluating this expression, we find:

V ≈ 616.62 m^3.

Rounding this value to the nearest integer, the volume of the frustum is approximately 617 m^3.

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The measure of the variable 'b' from the line is 11

Collinear points are points that lies on the same straight line. From the given diagram:

XY = YZ  (since Y is the midpoint of XZ)

where:

XY = 2b + 7

YZ = 3b - 4

Substitute the given parameters to have:

2b + 7 = 3b - 4

2b - 3b = -4 - 7

-b = -11

b = 11

Hence the measure of the value of b from the line is 11

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Answer:

The equilibrium point for the product (x,y) = (50,2300)

Step-by-step explanation:

The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.

From the question, we can identify the following;

S(x) = 300 + 40x

D(x) = 4300 - 40x

Now, at the equilibrium point, S(x) = D(x)

This means that;

300 + 40x = 4300 -40x

80x = 4300-300

80x = 4000

x = 4000/80 = 50

Now, we input the value of x into any of the equation of the demand and supply to get the quantity.

Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300

The equilibrium point for the product (x,y) = (50,2300)

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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The solution to the system, as an ordered triple is: (3, -4, 6).

To solve the following given system of equations:

2x + y + 3z = 20 --> eqn. 1

x + 2y - z = -11 --> eqn. 2

3x - 2z = -3 --> eqn. 3

Multiply equation 1 by 2 to get eqn. 4:

4x + 2y + 6z = 40 --> eqn. 4

Subtract eqn. 4 from eqn. 2:

x + 2y - z = -11 --> eqn. 2

4x + 2y + 6z = 40 --> eqn. 4

-3x - 7z = -51 --> eqn. 5

Add equations 3 and 5 together:

3x - 2z = -3 --> eqn. 3

-3x - 7z = -51 --> eqn. 5

-9z = -54

z = -54/-9

z = 6

Substitute the value of z into equation 5:

-3x - 7(6) = -51 --> eqn. 5

-3x - 42 = -51

-3x = -51 + 42

-3x = -9

-3x/-3 = -9/-3

x = 3

Find the value of y by substituting the values of x and z into equation 1:

2(3) + y + 3(6) = 20 --> eqn. 1

6 + y + 18 = 20

24 + y = 20

y = 20 - 24

y = -4

The solution as an ordered triple is: (3, -4, 6).

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Answer:

i think, THINK

in still air: 791

in wind: 90

im not too sure but its an answer!! if u get it wrong then not my fault ok

Answer:

Step-by-step explanation:

Let the perimeter of the square with length of n be Pₙ.

According to given table we have:

We can put this as a sequence:

Common difference is:

The recursive formula for this sequence is:

The final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

To translate the figure by <6,4>:

Add 6 to the x-coordinate of each point to get the new x-coordinate

Add 4 to the y-coordinate of each point to get the new y-coordinate

New coordinates:

A'(-3+6,-2+4) = (3,2)

C'(-4+6,-4+4) = (2,0)

B'(0+6,-4+4) = (6,0)

To dilate the figure K=4:

The coordinates x and y are multiplied by 4.

New coordinates:

A"(-34,-24) = (-12,-8)

C"(-44,-44) = (-16,-16)

B"(04,-44) = (0,-16)

Hence, the final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer: D - 14

Step-by-step explanation:

1 gallon = 2.15

So to find how many gallons is worth 30.10, divide by 2.15

30.10 ÷ 2.15 = 14

Answer:

Step-by-step explanation:

To find the required gallons of gas for 30.10$, you can use the following formula:

Required gallons of gas=Cost of required gallons of gas/cost of one gallon of gas

Here given that, the cost of required gallons of gas is 30.10$ and the cost of one gallon of gas is 2.15$

Now apply the formula:

Required gallons of gas = 30.10$/2.15$ = 14

Therefore, the required gallons of gas = 14

So 14 gallons of gas costs 30.10$

Option D is the correct answer.

Answer:

$75

Step-by-step explanation:

The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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Answer:

Step by step explanation:

well this is simble you just do it

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The decimal form of 2 2/5 can be written as,

2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4

Hence, the decimal form of 2 2/5 is 2.4.

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(a) 58 = 2(w + 5 + w)

(b)  I. The width of the rectangle is 12 cm.

II. The length of the rectangle is 17 cm.

III. The area of the rectangle is 204 cm².

Let's solve the problem step by step:

(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:

Perimeter = 2(length + width)

Substituting the values, we have:

58 = 2(w + 5 + w)

Simplifying the equation, we get:

58 = 2(2w + 5)

(b) Now let's solve for the width and length of the rectangle:

I. To find the width, we solve the equation:

58 = 2(2w + 5)

Dividing both sides by 2, we get:

29 = 2w + 5

Subtracting 5 from both sides, we have:

24 = 2w

Dividing both sides by 2, we find:

w = 12 cm

Therefore, the width of the rectangle is 12 cm.

II. To find the length, we substitute the value of the width into the equation:

Length = w + 5 = 12 + 5 = 17 cm

Therefore, the length of the rectangle is 17 cm.

III. The area of the rectangle can be calculated using the formula:

Area = length × width

Substituting the values, we have:

Area = 17 cm × 12 cm = 204 cm²

Therefore, the area of the rectangle is 204 cm².

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The quadratic function graphed is defined as follows:

y = x² - 10x + 9.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

From the graph, the roots are given as follows:

x = 1 and x = 9.

Hence the function as a product of it's linear factors is defined as follows:

y = a(x - 1)(x - 9)

y = a(x² - 10x + 9).

When x = 5, y = -16, hence the leading coefficient a is obtained as follows:

-16 = a(5² - 10(5) + 9)

-16a = -16

a = 1.

Thus the function is:

y = x² - 10x + 9.

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The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Answer:

d) 1/12

Step-by-step explanation:

The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.

Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:

= 3.75 × x

= 3.75x

Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:

= 5 + (3.25 × x)

= 5 + 3.25x

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