g) a car rental agency has ten mid-sized and fifteen compact cars on its lot, from which six will be selected. assuming that each is equally likely to be selected, and that they will be selected at random, what is the probability that exactly two mid-sized cars and four compact cars will be selected?

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{\pi }{6} \end{cases}\implies A=\cfrac{(\frac{\pi }{6})(6)^2}{2} \\\\\\ A=3\pi \implies A\approx 9.42~m^2[/tex]

Step-by-step explanation:0

The slope is 1/2, and the y-intercept is (0,-1).

The area shaded is what x could be

Answer: It meets at 90, and it passes through the midpoint.

Step-by-step explanation:

It isn't the first option because there is no distance between the line and it's bisector

It meets at AB because at a 90 degree angle because it perpendicular

Because of that, it can't also meet at a 180 degree angle

because its a bisector, it would not pass through A or B

It must meet line AB to bisect it

And because it bisects the line, it would also pass through the midpoint.

The correct inequality which is true when the value of x is -15 is,

⇒ x - 6 < - 1

⇒ - x - 6 > - 1

We have to given that;

To find inequality which is true when the value of x is -15.

Hence, Substitute x = - 15 in the inequality and find correct inequality as;

⇒ x - 6 > - 1

⇒ - 15 - 6 > - 1

⇒ - 21 > - 1

Which is not true.

⇒ - x - 6 < 1

⇒ - (- 15) - 6 < 1

⇒ 15 - 6 < 1

⇒ 9 < 1

Which is not true.

⇒ x - 6 < - 1

⇒ - 15 - 6 < - 1

⇒ - 12 < - 1

Which is true.

⇒ - x - 6 > - 1

⇒ - (- 15) - 6 > - 1

⇒ 15 - 6 > - 1

⇒ 9 > - 1

Which is true.

Thus, The correct inequality which is true when the value of x is -15 is,

⇒ x - 6 < - 1

⇒ - x - 6 > - 1

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The value of x for the same angle based on the information is 13.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle

Since angles 5 and 10 are the same, we can set them equal to each other:

91 - 2x = 5x

Simplifying this equation, we can add 2x to both sides:

91 = 7x

Then, we can divide both sides by 7 to solve for x:

x = 13

Therefore, the value of x for the same angle is 13.

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The Transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3

To shift the graph of the equation y=|1/2x-2|+3 one unit to the right, we can use a transformation of the form y=|1/2(x-1)-2|+3. This transformation will shift the graph one unit to the right by replacing x with (x-1) in the original equation.

To graph the transformed equation, we can start by finding the x- and y-intercepts. To find the y-intercept, we set x=0:

y=|1/2(0-1)-2|+3

y=|1/2(-1)-2|+3

y=|-1/2-2|+3

y=|-5/2|+3

y=5/2+3

y=11/2

Therefore, the y-intercept is (0, 11/2).

To find the x-intercept, we set y=0:

0=|1/2(x-1)-2|+3

-3=|1/2(x-1)-2|

-3=1/2(x-1)-2 or -3=-1/2(x-1)-2

-1=1/2(x-1) or -1=-1/2(x-1)

-2=x-1 or 0=x-1

x=-1 or x=1

Therefore, the x-intercepts are (-1, 0) and (1, 0).

Next, we can plot these points and draw the graph. The graph is symmetric about the vertical line x=1, as the absolute value function has this property.

Overall, the transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3.

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Answer:

C. (x+2)2=3

Step-by-step explanation:

Take the root of both sides and solve.

Both x2+4x-5=0 and (x+2)2=3 have the solution of x=1,-5

have a great day and thx for your inquiry :)

When comparing the two means of independent samples, we are allowed to pool the variances when the population variances are unknown, but assumed equal.

Pooling the variances is a statistical technique used when comparing means from independent samples. It involves combining the sample variances from both groups to estimate a common variance. This assumption of equal variances allows for a more accurate estimation of the standard error in the case of equal population variances.

When the population variances are unknown, we can conduct a statistical test, such as the t-test, assuming equal variances. This test uses the pooled variance estimate to calculate the standard error and determine the statistical significance of the mean difference between the two groups.

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To find the points where the height of the Gateway Arch is 100 meters, we need to solve the equation y = 100 for x.

Substituting y = 100 into the equation for the central curve of the arch, we get:

100 = 211.49 - 20.96 cosh (0.03291765x)

Rearranging the equation, we get:

cosh (0.03291765x) = (211.49 - 100) / 20.96

cosh (0.03291765x) = 5.21

Taking the inverse hyperbolic cosine of both sides, we get:

0.03291765x = acosh(5.21)

x = (1/0.03291765) acosh(5.21)

Solving for x using a calculator, we get:

x = ± 64.975

Therefore, the height of the Gateway Arch is 100 meters at the points (64.975, 100) and (-64.975, 100).

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Answer:

1: $85

2: $3.10

3: $9.75

4: $3.78

Step-by-step explanation:

1: 2 tickets = $34

 1 ticket = $17   (34 divided by 2)

17 x 5 = $85

2: 3 can = $.93

   0.93 / 3 = $0.31

0.31 x 10 = $3.10

3: 3 copies = $5.85

  5.85 / 3 = $1.95

$1.95 x 5 = $9.75

4: 4 containers = $2.52

2.52 / 4 = $0.63

0.63 x 6 = $3.78

Step-by-step explanation:

  One is twice as fast as the other     speeds are 2 x and x

      rate * time = distance

        (2x -x) * 50 = 750         x = 15 m/min      2x = 30 m/min

1.429

This is the answer to your problem

The solution of the expression is,

⇒ 0 + (7/11)√5

We have to given that;

Expression is,

⇒ (7 + √5) / (7 - √5) - (7 - √5) / (7 + √5)

Take LCM we get;

⇒ (7 + √5)² - (7 - √5)² / (7 - √5) (7 + √5)

⇒ (49 + 5 + 14√5) - (49 + 5 - 14√5) / (7² - √5²)

⇒ (28√5) / (49 - 5)

⇒ 28√5 / 44

⇒ 7√5 / 11

⇒ 0 + (7/11)√5

Thus, The solution of the expression is,

⇒ 0 + (7/11)√5

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Answer:

----------------------------

Use the formula:

We know that John drives a distance of 16 miles to work at a rate of m miles per hour.

So, the time it takes him to travel the full distance is:

On a certain day, the car stops after only v miles. So, the distance John still needs to travel is:

We also know that he will be traveling at the same rate, so we can use the formula again:

To find the time left, we can rearrange the formula:

The final result of the expression is -12,173/10,083. First, let's find the sum of 2/9 and -3/7. To add fractions, we need a common denominator. The least common multiple of 9 and 7 is 63.

To simplify the given expression, let's break it down step by step:

The sum of 2/9 and -3/7 is:

(2/9) + (-3/7)

To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 9 and 7, which is 63.

(2/9) + (-3/7) = (2 * 7)/(9 * 7) + (-3 * 9)/(7 * 9)

= 14/63 - 27/63

= (14 - 27)/63

= -13/63

The difference of 3/7 and -13/23 is:

(3/7) - (-13/23)

Again, we need a common denominator, which is the LCM of 7 and 23, which is 161.

(3/7) - (-13/23) = (3 * 23)/(7 * 23) - (-13 * 7)/(23 * 7)

= 69/161 + 91/161

= (69 + 91)/161

= 160/161

Now, we subtract the second result from the first result:

(-13/63) - (160/161)

To subtract fractions, we need a common denominator, which is the LCM of 63 and 161, which is 10,083.

(-13/63) - (160/161) = (-13 * 161)/(63 * 161) - (160 * 63)/(161 * 63)

= -2,093/10,083 - 10,080/10,083

= (-2,093 - 10,080)/10,083

= -12,173/10,083.

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When x = 10, b takes the value 1. The values of a and b when x = 10 are a = 25 and b = 1.

To find the values of a and b when x = 10, we can substitute x = 10 into the given expressions for a and b and simplify the equations.

a = 5x/2

Replacing x with 10:

a = 5(10)/2

a = 50/2

a = 25

So, when x = 10, a takes the value 25.

b = 2x*(x - 5)/10x

Replacing x with 10:

b = 2(10)(10 - 5)/(1010)

b = 2(10)(5)/(100)

b = 205/100

b = 100/100

b = 1.

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Step-by-step explanation:

(3j - 5k^3) ( 3j + 5k^3)  =  9j^2 - 25k^6

The approximate number of customers (waiting and being served) at the carwash is 3.

To determine the number of customers (waiting and being served) at the carwash, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.

In this case, the average arrival rate is 9 customers per hour, and the average waiting time is given as 23 minutes (which is equivalent to 23/60 = 0.3833 hours).

Using Little's Law, we can calculate the average number of customers in the system:

Average number of customers = Average arrival rate * Average time spent in the system

Average number of customers = 9 customers/hour * 0.3833 hours

Average number of customers = 3.4497 customers

Since we can't have fractional customers, we round the value to the nearest whole number.

Therefore, the approximate number of customers (waiting and being served) at the carwash is 3.

It's important to note that this calculation assumes steady-state conditions and that the arrival and service distributions are not known.

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Answer:

20

Step-by-step explanation:

16 / 20 = 0.80

0.80 = 80%

Therefore, the probability that the first card is a diamond or the second card is a face card is approximately 0.3039.

We can solve this problem by using the addition rule of probability.

The probability of the first card being a diamond is 13/52 (since there are 13 diamonds in a standard deck of 52 cards). The probability of the second card being a face card is 12/51 (since there are 12 face cards left in the deck after the first card is drawn).

To find the probability that either event occurs, we add the probabilities and subtract the probability of both events happening together (since we only want to count that once):

P(diamond or face card) = P(diamond) + P(face card) - P(diamond and face card)

P(diamond or face card) = 13/52 + 12/51 - (3/51) [since there are 3 face cards that are also diamonds]

Simplifying the expression, we get:

P(diamond or face card) = 0.3039

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The number of zeroes or x-intercepts of a polynomial function is related to its highest power, which is determined by the degree of the polynomial. Let's consider a polynomial of degree "n" where "n" is a positive integer.

The minimum number of zeroes or x-intercepts a polynomial can have is zero. This occurs when all the terms of the polynomial have non-zero coefficients and there are no factors that would cause the polynomial to equal zero. For example, a polynomial of degree 2, such as f(x) = x^2 + 1, has no zeroes.

The maximum number of zeroes or x-intercepts a polynomial of degree "n" can have is "n". This is known as the Fundamental Theorem of Algebra, which states that a polynomial of degree "n" can have at most "n" distinct zeroes.

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a) The radius of convergence is also 1, since it is the same as the radius of convergence of ln(1+x).

a) We can find a power series representation for f(x) = ln(1+x) by using the formula:

ln(1 + x) = ∑(-1)^(n-1) * x^n / n for |x| < 1

So, the power series representation for ln(1+x) is:

ln(1 + x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...

The radius of convergence is 1, since the series converges for |x| < 1 and diverges for |x| > 1.

b) To find a power series for f(x) = xln(1+x), we can use the product rule of power series:

xln(1 + x) = x * [x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...]

= x^2 - x^3/2 + x^4/3 - x^5/4 + x^6/5 - ...

So, the power series representation for f(x) = xln(1+x) is:

f(x) = xln(1+x) = ∑(-1)^(n-1) * x^(n+1) / n for |x| < 1

c) To find a power series for f(x)ln(x^2 + 1), we can use the product rule of power series again:

f(x)ln(x^2 + 1) = [x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...] * ln(x^2 + 1)

= [xln(x^2 + 1)] - [x^2 ln(x^2 + 1)]/2 + [x^3 ln(x^2 + 1)]/3 - [x^4 ln(x^2 + 1)]/4 + [x^5 ln(x^2 + 1)]/5 - ...

We already have a power series for xln(1+x), which is the same as xln(x^2+1) for |x| < 1. So, we can substitute it in the above series:

f(x)ln(x^2 + 1) = ∑(-1)^(n-1) * x^(2n+1) / (2n+1) * [1 - 1/2 + 1/3 - 1/4 + 1/5 - ...]

= ∑(-1)^(n-1) * x^(2n+1) / (2n+1) * ln(x^2 + 1)

The radius of convergence of this power series is also 1, since it is the same as the radius of convergence of ln(1+x) and xln(1+x).

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The height of the cylinder is approximately 7.94 meters when rounded to the nearest tenth.

How did this do?

The surface area of a cylinder can be calculated using the formula:

SA = 2πr^2 + 2πrh

where r is the radius of the base and h is the height of the cylinder.

We are given the diameter of the cylinder's base, which is 8 m. The radius is half the diameter, so:

r = 8 m / 2 = 4 m

Substituting this value for r, and the given value for SA into the formula, we get:

256.224 m² = 2π(4 m)^2 + 2π(4 m)h

Simplifying this equation:

256.224 m² = 32π + 8πh

256.224 m² - 32π = 8πh

h = (256.224 m² - 32π) / (8π)

h ≈ 7.94 m (rounded to the nearest tenth)

To express the radius of a circle, denoted by r, in terms of the length of the chord (l) and the distance of the chord from the center of the circle (h), we can use the following approach:

In a circle, the perpendicular distance from the center to a chord bisects the chord. This means that the distance from the center to the midpoint of the chord is equal to h/2. Now, consider the right triangle formed by the radius (r), the distance from the center to the midpoint of the chord (h/2), and half of the chord length (l/2). According to the Pythagorean theorem, the square of the radius is equal to the sum of the squares of the other two sides of the triangle.

Using this information, we can write the equation:

r^2 = (h/2)^2 + (l/2)^2

Simplifying the equation:

r^2 = h^2/4 + l^2/4

Taking the square root of both sides to solve for r:

r = √(h^2/4 + l^2/4)

Therefore, the expression for the radius (r) in terms of the length of the chord (l) and the distance of the chord from the center (h) is r = √(h^2/4 + l^2/4).

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Answer:

p=$16.5

Step-by-step explanation:

By using the distributive Property, you can say:

5p-15=63

Then add 15 on both sides to make the equation balanced:

5p=78

Then divide by 5:

p=78/5=$16.5

The equation that can be used to determine the reference angle, r, if θ = 7π/12 is option (b) r = π - θ.

A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we need to subtract the angle from either π/2 or π (depending on which quadrant the angle is in).
In this case, 7π/12 is in the second quadrant (between π/2 and π). Therefore, we subtract 7π/12 from π to get the reference angle:

r = π - θ
r = π - 7π/12
r = (12π/12) - (7π/12)
r = 5π/12

So the reference angle, r, for θ = 7π/12 is 5π/12.
Note that option (a) r = θ is incorrect because this would give the same angle as θ, not the reference angle. Option (c) r = θ - π is incorrect because it would give a negative angle, which is not an acute angle. Option (d) r = 2π - θ is incorrect because it would give an angle in the fourth quadrant, which is not the reference angle for an angle in the second quadrant.

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There are 3x = 3(28) = 84 kiwis.next, we are told that the ratio of strawberries to kiwis is 5:4.

let's start by using the second piece of information to find the number of kiwis. if the ratio of kiwis to plums is 3:2, then we can represent the number of kiwis as 3x and the number of plums as 2x. we are told that there are 56 plums, so we can solve for x:

2x = 56x = 28 let's represent the number of strawberries as 5y and the number of kiwis as 4y. we already know that there are 84 kiwis, so we can solve for y:

4y = 84

y = 21

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The statements about the given parabola that are true are:

The form of a parabola is :

y = a ( x - h ) ² + k

This means that the statement that the vertex is (-2, 4) is true because the vertex is ( h, k ).

The focus is ( h,  k - p ) which would be ( -2 , 1 / 2 ). This is shown in option A.

The Directrix is:

y = 4 + 7/2

= 15 / 2

This is shown in option C.

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Answer:

S=2t

or

T=1/2 S