The area of a sector of a circle with a central angle of 5 radians is 15cm². Find the radius of the circle.
Do not round any intermediate computations. Round your answer to the nearest tenth.

Option D, F(x) = 1/x-4, is the rational function that best fits the graph.

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator.

The graph features a vertical asymptote at x = 4 and a horizontal asymptote at y = 0, as can be seen by looking at it.

Option A, F(x) = 1/4x, has a horizontal asymptote at y = 0, but does not have a vertical asymptote at x = 4.

Option B, F(x) = 4/x, has a vertical asymptote at x = 0, but not at x = 4.

Option C, F(x) = 1/x+4, has a vertical asymptote at x = -4, but not at x = 4.

Option D, F(x) = 1/x-4, has a vertical asymptote at x = 4, and does not have any other vertical asymptotes.

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Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

Answer:

Step-by-step explanation:

To solve this problem, we can use the formula for the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given the length of two sides of the triangle (the legs) and we need to find the length of the hypotenuse.

Let's label the sides of the triangle:

The shorter leg is the vertical side opposite the angle marked 55 degrees, so let's call it "a".

The longer leg is the horizontal side adjacent to the angle marked 55 degrees, so let's call it "b".

The hypotenuse is the side opposite the right angle, so let's call it "c".

Using trigonometry, we can determine the value of "a" and "b":

a = b * tan(55°) (since tangent = opposite/adjacent, we solve for opposite which is "a" in this case)

a = 100 * tan(55°) = 100 * 1.428 = 142.8

b = 100

Now, we can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = 142.8^2 + 100^2

c^2 = 20484.84 + 10000

c^2 = 30484.84

c = sqrt(30484.84)

c ≈ 174.6

Therefore, the length of the hypotenuse is approximately 174.6 units (the units are not given in the problem, but we can assume they are consistent with the units used for the given values of "a" and "b").

The problem does not specify the orientation or scale of the graph, but we can assume that it is a right triangle with the angle marked 55 degrees in the upper left corner.

The vertical side (the shorter leg) of the triangle should be labeled with a length of approximately 142.8 units (assuming the units used for the problem are consistent with the values given for "a" and "b"). The horizontal side (the longer leg) should be labeled with a length of 100 units.

The hypotenuse (the side opposite the right angle) should be drawn as a diagonal line connecting the endpoints of the vertical and horizontal sides. The hypotenuse should be labeled with a length of approximately 174.6 units.

The angle marked 55 degrees should be labeled as such, and the other two angles of the triangle (the right angle and the angle opposite the longer leg) should be labeled accordingly.

Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

The unitary method is a mathematical approach where issues are solved by determining a single unit rate. To relate various quantities to one another, proportions must be used. This approach is frequently employed in issues involving direct and inverse proportionality. In inverse proportionality, the product of the two quantities is constant, whereas in direct proportionality, the two numbers fluctuate in the same ratio.

given

We must first determine the total number of cups of milk served in both March and April in order to calculate the total number of quarts of milk served in both months.

4080 cups of milk totaled from 2420 + 1660 cups.

We can convert the total number of cups to quarts by dividing by 4 because 1 quart equals 4 cups:

4080 cups of milk divided by 4 equals 1020 quarts total.

Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

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a) The first four nonzero terms of the power series for f(x) about x=0 are

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is (-2)^n (2x)^(2n) / (2n)!

b) The interval of convergence of the power series is (-∞, ∞).

c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula

f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ

where fⁿ(0) denotes the nth derivative of f evaluated at x=0.

In this case, we have

f(x) = e^6(-2x^2)

fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)

So, we can write the power series as

f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)

= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)

To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula

f(0) = e^6

f'(0) = 0

f''(0) = 24

f'''(0) = 0

So, the first four nonzero terms of the power series are:

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is

(-2)^n (2x)^(2n) / (2n)!

b) To find the interval of convergence of the power series, we can use the ratio test

lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|

= lim [n→∞] |-4x^2/(2n+1)(2n+2)|

= lim [n→∞] 4x^2/(2n+1)(2n+2)

Since this limit depends on the value of x, we need to consider two cases

i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.

ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value

|4x^2/(2n+1)(2n+2)| < 1

This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).

c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].

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Answer:

Here is a diagram and transition matrix for this case:

Diagram:

        +---(0.65)---> State 1 (work)

        |

Start ---+

        |

        +---(0.35)---> State 2 (procrastinate)

                  |

                  +---(0.15)---> State 1 (work)

                  |

                  +---(0.85)---> State 2 (procrastinate)

Transition matrix:

         |  State 1  |  State 2  |

----------+-----------+-----------+

State 1   |   1.00    |   0.00    |

----------+-----------+-----------+

State 2   |   0.15    |   0.85    |

----------+-----------+-----------+

In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Both rectangular prisms  will move at the same speed and volume of A > volume of B

What is rectangular prism ?

A rectangular prism is a three-dimensional solid shape that consists of six rectangular faces. It is also known as a rectangular cuboid, and it is a special case of a parallelepiped, which is a six-faced polyhedron where each face is a parallelogram. The rectangular prism has parallel and congruent rectangular bases that are connected by rectangular faces that are perpendicular to the bases.

The rectangular prism has several important properties. One of the most important is its volume, which is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the rectangular prism.

Comparing their masses and volumes.
If the mass is the same for both rectangular prisms, then they will move at the same speed if pushed by the same amount of force. The mass of an object is a measure of the amount of matter it contains, and since both prisms have the same mass, they contain the same amount of matter. The force required to move an object is proportional to its mass, so if both objects have the same mass, they will require the same amount of force to move. Therefore, they will move at the same speed.

We can compare their volumes using the inequality sign:

volume of A > volume of B

This is because the area of the base of A is greater than the area of the base of B, and the height of A is less than the height of B. So, A has a greater volume than B.

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Answer:

Option C is the correct answer. 0.17 is the probability that a randomly selected student smokes out of 500 students, given 85 smoke.

By dividing the total number of students observed (500) by the number of students who smoke (85) in this scenario, it is possible to estimate the probability of smoking among the 500 students.

This results in a ratio of 0.17, or 17%. The estimated likelihood that a randomly chosen student smokes is therefore 0.17, meaning that roughly 17 out of every 100 students in the population smoke. It is crucial to remember that this is only an estimate, and the true probability could change slightly depending on the size and sampling method.

The estimated probability does, however, have a tendency to converge to the true probability when the sample size is sufficient.

Hence, the probability that a randomly selected student smokes  is 0.17

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The calculated coordinates of U if STUV is a kite is (10, 18)

From the question, we have the following parameters that can be used in our computation:

The figute of a kite

Also, we have

S = (0, 18)

And the distance SU to be

SU = 10

If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)

So, we have

U = (0 + 10, 18)

Evaluate

U = (10, 18)

Hence, the coordinates of U if STUV is a kite is (10, 18)

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Answer:

2%

Step-by-step explanation:

Given,P = $73000

A = $104000

T = 18 years, Compounded annually.

To find: r%

Soln: By formula, A = 73000*(1+r/100)^18

=> (104/73)^1/18 = (100+r)/100

=> 1.0198 = 100+r/100

=> 101.98 -100 = r

=> 1.98 = r

To the nearest percent, 2 = r

Hence, Rate of interest = 2%

The probability of the randomly chosen American passenger car is a uniformly distributed random variable ranging from 1,557 pounds to 4,665 pounds is given as:

In statistics, a uniform distribution is a kind of probability distribution where all possible outcomes have an identical likelihood of occurring. Because there is an equal chance of getting a heart, club, diamond, or spade, a deck of cards has uniform distributions.

PDF of Uniform Distribution f(x) = 1/(b-a) for a <x<b

b = Maximum Value

a = Minimum Value

Mean = (a + b)/2

Standard Deviation [tex]\sqrt{((b- a)^2/12)}[/tex]

a) Mean = a + b/2=3111

mean weight of a randomly chosen vehicle is 3111

b) Standard Deviation = [tex]\sqrt{((b- a)^2/12)}[/tex] =897.2023

f(x) = 1/(b-a)

= 1/(4665-1557)

=1/3108

= 0.0003

the standard deviation of a randomly chosen vehicle is 0.0003.

c) P(X < 1946) = (1946-1557) x f(x)

= 389 x 0.0003

= 0.1167

the probability that a vehicle will weigh less than 1,946 pounds is 0.1167.

d) P(X > 4455) = (4665-4455) x f(x)

=210 x 0.0003

= 0.063

the probability that a vehicle will weigh more than 4,455 pounds is 0.063.

e) To find P(a< X< b)=( b - a) x

f(x) P(1946 < X < 4455)

= (4455-1946) x f(x)

=2509 x 0.0003

= 0.7527

the probability that a vehicle will weigh between 1,946 and 4,455 pounds is 0.7527.

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(a) By using the exponential density function, the probability that a customer warts less than a second for credit card approval is 0.334

(b) The probability that a customer waits more than 3 seconds is 0.154

(c) The minimum approval time for the slowest 5% of transactions is 4.013 seconds

(a) To find the probability that a customer waits less than a second for credit card approval, we need to use the exponential density function:

f(x) = [tex]\lambda e^{-\lambda x}[/tex]

Where λ is the rate parameter, which in this case is the reciprocal of the mean approval time. So, λ = 1/1.6 = 0.625.

The probability that a customer waits less than a second can be calculated by integrating the density function from 0 to 1:

P(X < 1) = ∫[tex]0^1 \lambda e^{-\lambda x}[/tex] dx

P(X < 1) = [tex][-e^{-\lambda x}]0^1[/tex]

P(X < 1) = [tex]-e^{(-0.625)}[/tex] + 1

P(X < 1) = 0.334

Therefore, the probability that a customer waits less than a second for credit card approval is 0.334.

(b) To find the probability that a customer waits more than 3 seconds for credit card approval, we can use the same exponential density function and integrate from 3 to infinity:

P(X > 3) = ∫[tex]3^{\infty} \lambda e^{-\lambda x}[/tex] dx

P(X > 3) = [[tex]-e^{-\lambda x}[/tex])][tex]3^{\infty}[/tex]

P(X > 3) = [tex]e^{-1.875}[/tex]

P(X > 3) = 0.154

Therefore, the probability that a customer waits more than 3 seconds for credit card approval is 0.154.

(c) We can use the exponential distribution's inverse function to find this value:

P(X > x) = 0.05

[tex]e^{-\lambda x}[/tex] = 0.05

-xλ = ln(0.05)

x = ln(0.05)/(-λ)

x = ln(0.05)/(-0.625)

x = 4.013 seconds

Therefore, the minimum approval time for the slowest 5% of transactions is 4.013 seconds.

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Answer: Somewhere around 40%, write 0.4.

Step-by-step explanation:

I took all of the outcomes from the games got the. probabilities of winners and got 40%.

Answer:

35 minutes

Step-by-step explanation:

because it is composure

the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

Let X be the weight of a small Starbucks coffee. We are given that X is normally distributed with mean [tex]$\mu=385$[/tex] grams and standard deviation [tex]$\sigma=8$[/tex].

We want to find the weight that corresponds to each of the following events:

a) The weight is less than 380 grams.

b) The weight is between 375 and 395 grams.

c) The weight is greater than 400 grams.

To solve these problems, we first standardize the distribution by finding the corresponding z-scores using the formula:

[tex]$z=\frac{X-\mu}{\sigma}$$[/tex]

a) The weight is less than 380 grams.

We want to find P(X<380). We can find the z-score for X=380 as follows:

[tex]$z=\frac{380-385}{8}=-0.625$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z<-0.625)=0.266. Therefore,

[tex]$P(X < 380)=P\left(Z < -\frac{0.625}{1}\right)=0.266$$[/tex]

b) The weight is between 375 and 395 grams.

We want to find [tex]$P(375 < X < 395)$[/tex]. We can find the z-scores for X=375 and X=395 as follows:

[tex]$z_1=\frac{375-385}{8}=-1.25,\quad z_2=\frac{395-385}{8}=1.25$$[/tex]

Using a standard normal table or calculator, we find that the probability P(-1.25<Z<1.25)=0.7887. Therefore,

[tex]$P(375 < X < 395)=P\left(-1.25 < Z < 1.25\right)=0.7887$$[/tex]

c) The weight is greater than 400 grams.

We want to find P(X>400). We can find the z-score for X=400 as follows:

[tex]$z=\frac{400-385}{8}=1.875$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z>1.875)=0.0304. Therefore,

[tex]$P(X > 400)=P\left(Z > \frac{1.875}{1}\right)=0.0304$$[/tex]

Therefore, the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

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When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

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Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.

Outside the sphere, the potential is given by

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]

where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]

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Answer:

Step-by-step explanation:

In the boys triangle:

  [tex]tanx=\frac{56}{48}[/tex]

        [tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]

Because triangles are similar:

   [tex]tan 49.8=\frac{h}{32}[/tex]

[tex]h=32tan49.8 = 37.3[/tex]

a) The drawing of all data points on a 2D plane is illustrated below.

b) The angle in between the five other points is 27

c) The matrix outer product for X is R = XXT.

d) The matrix outer product can also be calculated via R is (2,27)

The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.

To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.

Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.

The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.

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The correct research hypothesis and distribution is directional, t-test for independent means.

The research hypothesis that "people can hear better when they have just eaten a large meal" is a directional hypothesis because it predicts the direction of the effect (i.e., hearing ability will improve after a large meal).

The appropriate statistical test to use would be a t-test for independent means, which compares the means of two independent groups to determine if there is a statistically significant difference between them.

Therefore, the correct answer is B. Directional; t-test for independent means.

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The minimum value of f subject to the given constraint is -62.42 (abs min).

We need to find the minimum and maximum values of f(x,y) = 2x-5y subject to the constraint g(x,y) = x2+3y2 = 111.

Using Lagrange multipliers, we solve the equations:

∇f= λ∇g and g(x,y)  = 111.

This gives,

2 = λ2x    (1) equation.

-5 = λ6y   (2) equation.

From (1) we have λ=1/x. Substituting this into (2)

we have x=-6y/5 (3).

By substituting (3) into constraint g(x,y) we have

                     (-6y/5)2+3y2 = 111

                   y2(-36/25 + 3) = 111

                                         y = ±5√37/√13.

We have given some corresponding points in question (-6√37/√13, 5√37/√13) and (6√37/√13, -5√37/√13).

Evaluating f at these critical points:

f(-6√37/√13, 5√37/√13)

= 13√37/√13

≈ -62.42 (abs min)

f(6√37/√13, -5√37/√13)

=  37√37/√13

≈ 62.42  (abs max)

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Full Question:

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=2x−5y subject to the constraint x2+3y2=111, if such values exist.

Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

Answer:

p < -4

Step-by-step explanation:

-6(4p+5) > 34 - 8p

-24p - 30 > 34 - 8p

-16p - 30 > 34

-16p > 64

p < -4

There is no value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

The proportion for this problem is defined by the equation presented as follows:

(x^2-x-12)/(x+5) = x-6.

As the measures are proportional, we can apply cross multiplication, hence:

x² - x - 12 = (x + 5)(x - 6)

x² - x - 12 = x² - x - 30

-12 = -30.

-12 = -30 is a false statement, hence there is no value of x which can solve the proportion (x^2-x-12)/(x+5)=x-6 presented in this problem.

The problem asks for the value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

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Answer:

True

Step-by-step explanation:

Since x = 3 since we are given that f(3) = 16, x = 3.

The equation is:

[tex]f(x) = x^{2} + 2x + 1[/tex]

and x = 3, we can easily sustitute x with 3. When we do so, our equation will look like:

[tex]f(3) = 3^{2} + 2(3) + 1[/tex]

Now, we will solve.

3^2 is = 9

2(3) = 6

Now, we will plug into the equation:

[tex]f(3) = 9 + 6 + 1[/tex]

Combine like terms (constants)

[tex]f(3) = 16[/tex]

Answer:

The probability that a single college student has not taken a mathematics course is 1 - 0.8 = 0.2.

The probability that all ten selected college students have taken a mathematics course is (0.8)^10 = 0.1074 (rounded to four decimal places).

Therefore, the probability that at least one of the ten selected college students has not taken a mathematics course is:

1 - 0.1074 = 0.8926 (rounded to four decimal places).

So the answer is 0.8926, which is closest to option C (0.7927).

(please mark my answer as brainliest)

Answer:

Step-by-step explanation:

i think it B

Answer:

y=9/x  => proportional

y = x - 12 ==> non-proportional

h = 3d ==> proportional

f = 1/3 e = proportional

Step-by-step explanation:

A proportional equation is of the general form

y = kx (directly proportional) or

y = k/x  (inversely proportional)

k is known as the constant of proportionality

y = 9/x ==> k = 9  proportional
y = x - 12  cannot be expressed as y = kx or y = k/x

h = 3d ==> k = 3  proportional

f = 1/3 e ==> k = 1/3   proportional