Suppose 15% of the population are 62 or over, 27% of those 62 or over have loans, and 54% of those under 62 have loans. Find the probabilities that a person fits into the following categories. (a) 62 or over and has a loan (b) Has a loan (c) Are the events that a person is 62 or over and that the person has a loan independent?

Answer:

a) The person who washed the most of the laundry is Mrs Smith

b) 4/15 of the laundry is left to wash

Step-by-step explanation:

Mrs. Smith washed 2/5 of her laundry. Her son washed 1/3 of it.

a) Who washed most of the laundry?

We convert the fraction of laundry each person washed to decimal

Mrs Smith = 2/5 = 0.4

Her son = 1/3 = 0.333

Therefore, the person who washed the most of the laundry is Mrs Smith

b) How much of the laundry still needs to be washed?

Let us total laundry = 1

=1 - ( 2/5 + 1/3)

Lowest Common Denominator is 15

=1- (3 × 2 + 5 × 1/15)

= 1 - (6 +5/15)

=1 - 11/15

= 4/15

The limits are,

(a) lim(x→0) 4x/(x² + 1) = 0

(b) lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1) = ((1 + √(5))(3 - i))/10

(a) To find the limit of lim(x→0) 4x/(x² + 1), we can directly substitute 0 for x in the expression:

lim(x→0) 4x/(x² + 1) = (4 × 0)/(0² + 1) = 0/1 = 0

Therefore, the limit is 0.

(b) To find the limit of lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1), we can again substitute -1 for z in the expression:

lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1) = (1 + sqrt(2 - 2(-1) + (-1)^2))/(2 - i(-1) - 1)

= (1 + √(2 + 2 + 1))/(2 + i + 1)

= (1 + √(5))/(3 + i)

To simplify this expression further, we need to rationalize the denominator. We can multiply the numerator and denominator by the conjugate of the denominator, which is (3 - i):

lim(z→-1) (1 + √(5))/(3 + i) × (3 - i)/(3 - i)

= ((1 + √(5))(3 - i))/(9 - i²)

= ((1 + √(5))(3 - i))/(9 + 1)

= ((1 + √(5))(3 - i))/10

Therefore, the limit is ((1 + √(5))(3 - i))/10.

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The question is -

Find the following limits:

(a) lim(x->0) 4x/(x^2 + 1)

(b) lim(z->-1) (1 + sqrt(2 - 2z + z^2))/(2 - iz - 1)

The outcome of the race between Alpha and Beta, as described by their parametric equations, is that Beta moves faster but loses. Although Beta has a higher speed, Alpha consistently maintains a higher vertical position, leading to Alpha winning the race.

To determine the outcome of the race between Alpha and Beta, let's compare their positions using the given parametric equations:

Alpha's position:

[tex]x_{alpha} = 3t - 4sin(t)\\y_{alpha}= 3 - 3cos(t)[/tex]

Beta's position:

[tex]x_{beta} = 3t - 4sin(t)\\y_{beta} = 3 - 4sin(t)[/tex]

From the equations, we can see that the x-coordinate of both Alpha and Beta is the same, given by 3t - 4sin(t). Therefore, their horizontal positions are identical throughout the race.

To determine the vertical positions, we compare their y-coordinates. Alpha's y-coordinate is given by 3 - 3cos(t), while Beta's y-coordinate is given by 3 - 4sin(t).

Since cos(t) ranges from -1 to 1, and sin(t) ranges from -1 to 1, we can observe the following:

For Alpha, the y-coordinate (3 - 3cos(t)) ranges from 0 to 6, inclusive.

For Beta, the y-coordinate (3 - 4sin(t)) ranges from 2 to 4, inclusive.

Based on the range of their y-coordinates, we can conclude that Beta remains at a higher position throughout the race. Therefore, the correct answer is:

(D) Beta moves faster but loses.

Despite Beta moving faster, it loses the race because Alpha consistently maintains a higher vertical position.

Therefore, the outcome of the race between Alpha and Beta, as described by their parametric equations, is that Beta moves faster but loses. Although Beta has a higher speed, Alpha consistently maintains a higher vertical position, leading to Alpha winning the race.

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Answer:

The expected value of x ; E(x) = 1

Step-by-step explanation:

F(x) = 1/8 for 0 ≤ x ≤ 4

To prove that it is a probability density function we will find E(x )

attached below is the required prove

It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is  probability density function

The expected value of X = 1

Answer:

197.9

Step-by-step explanation:

The formula for circumference is 2(pi)r   and r is the radius

The diameter is two times the size of the radius, so by dividing the diameter by two, you can get the radius

So, r=63/2

r= 31.5

That means that 2(pi)(31.5) is the circumference

2(pi)(31.5) = 197.9 (rounded to the nearest tenth)

Answer:

No no don't click the link

Answer:

The biggest difference between exponential and linear functions is that linear functions change at a constant rate, while exponential functions change at a rate proportional to it's value, or exponent.

Basically, that's also what separates exponential functions from all others. It's the only function that changes at a rate proportional to its exponent.

Step-by-step explanation:

Answer:

I believe the answer is (A)

*Substituting the x and y values from the table into the equation(A) will balance the right side of the equation to the left side of the equation.

Answer:

Fibonacci

Step-by-step explanation:

the Fibonacci sequence

The total vertical distance traveled by the rubber ball, assuming it bounces indefinitely, is approximately 85.71 feet.

To find the total vertical distance traveled, we need to sum up the heights achieved by the ball during each bounce. The ball initially drops from a height of 26 feet, so we start with this value. On each bounce, the ball rebounds up 62% of its previous height. This means that after the first bounce, the ball reaches a height of 26 feet * 0.62 = 16.12 feet.

For subsequent bounces, we continue to multiply the previous height by 0.62 to find the new height. Therefore, after the second bounce, the height becomes 16.12 feet * 0.62 = 9.99 feet.

We can see that the heights achieved during each bounce form a geometric sequence with a common ratio of 0.62. The sum of an infinite geometric sequence can be calculated using the formula,

Sum = a / (1 - r), first term is a and 'r' is the common ratio is r.

In this case, 'a' is the initial height of 26 feet and 'r' is 0.62. Plugging these values into the formula, we get,

Sum = 26 / (1 - 0.62) = 26 / 0.38 ≈ 68.42 feet.

Therefore, adding all the distances,

Distance = 68.42 + 9.99 + 16.12

Distance = 85.71 feet, total vertical distance traveled by the rubber ball, rounded to two decimal places, is approximately 85.71 feet.

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Answer: $93649

Step-by-step explanation:

Since this is an exponential growth problem, then we can use the equation 50,000(1.04)^16. Solve it and you get 93649.06228. Round to the nearest dollar, which is probably whole number, so it is 93649.

Answer:

67 degrees for both of the other angles or 46 degrees and 88

Step-by-step explanation:

An isosceles triangle has two angle that are the same size so it could only be these.

The total number of people surveyed is 75.

The first step is to determine the number of people who had 4 or more rides that preferred a window seat.

= Total number of people that had four or more rides - total number of people who had 4 or more rides that prefer aisle

= 40 - 25 = 15

Total number of people that prefer the window seats= 15 + 20 = 35

Total number of people = total number of people that prefer the window seat + total number of people who prefer the aisle

= 35 + 40 = 75

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Answer:

216

Step-by-step explanation:

Answer:

72yd

Step-by-step explanation:

Hope that helps

hsobsnsjns

Answer:

180in3 (180 inch cubed)

Step-by-step explanation:

12 x 5 x 3

Answer: I would assume the answer would be 180

Step-by-step explanation: The formula for volume is Length x Width x Height. So multiply all the number above and the answer will be 180

Answer:

8,395

Step-by-step explanation:

21 x 400 = 8,400

is = x

8, 400 - 5 = 8,395

difference = -

Brainlist Pls!

Answer:

1666.70

Step-by-step explanation:  10,000/6=1666.70

The value of 'm' for which (x + 4) is a factor of the polynomial [tex]5x^3 + 18x^2 + mx + 16[/tex] is -4.

To find the value of 'm' for which the expression (x + 4) is a factor of the polynomial[tex]5x^3 + 18x^2 + mx + 16[/tex], we can apply the factor theorem. According to the factor theorem, if (x + 4) is a factor of the polynomial, then the polynomial evaluated at (-4) should be equal to zero.

Substituting (-4) into the polynomial, we get:

[tex]5(-4)^3 + 18(-4)^2 + m(-4) + 16 = 0[/tex]

-320 + 288 + (-4m) + 16 = 0

-16 + (-4m) = 0

Simplifying the equation, we have:

-4m - 16 = 0

-4m = 16

m = 16 / -4

m = -4

Therefore, the value of 'm' for which (x + 4) is a factor of the polynomial [tex]5x^3 + 18x^2 + mx + 16[/tex] is -4.

By substituting -4 for 'm' in the given polynomial, we obtain:

[tex]5x^3 + 18x^2 - 4x + 16[/tex]

When this polynomial is divided by (x + 4), the remainder will be zero, confirming that (x + 4) is indeed a factor.

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Answer:

thx for the points

Step-by-step explanation:

Answer:

Where is the question tho whaaAAaaaa

Answer: your answer should be 50%

Step-by-step explanation: This is because there are only four marbles in the bag total and only 2 are blue and only 2 are green so your chances of pulling out either is 50%

Answer:

33%

Step-by-step explanation:

2 blue marbles + 2 green marbles = 4 marbles

1st draw for blue:   2/4               (2 blue marbles out of 4 marbles)

2nd draw for green:   2/3          (1 less marble from 4, marble not put back in)

2/4  x  2/3   = 4/12 = 1/3 = 0.33 or 33%

Answer:

x = 10.52 m

Step-by-step explanation:

Given that,

Length of a park = 90 m

Width of a park = 60 m

Area, A = 9000 m²

A uniform strip borders all four sides of the park for parking. We need to find the width of the strip. Let it is x. Now the area becomes,

(90+2x)(60+2x) = 9000

[tex]4x^2 +120x +180x =5400 = 9000\\\\x=10.52\ m[/tex]

So, the width of the strip is equal to 10.52 m.

Answer:

100 i think

Step-by-step explanation:

Answer: One answer

Step-by-step explanation:

Given the function: f(x,y) = 3x^7 + 4y^7 + 12To verify that f_xy = f_yx, we need to find the partial derivatives of the given function with respect to x and y. We can find them as follows: ∂f/∂x = 21x^6 ∂f/∂y = 28y^6

Now, to verify that f_xy = f_yx, we need to find f_xy and f_yx. We can find them as follows: f_xy = ∂^2f/∂y∂x = ∂/∂y(∂f/∂x) = ∂/∂y(21x^6) = 0 (since we have no y terms in the derivative of ∂f/∂x) f_yx = ∂^2f/∂x∂y = ∂/∂x(∂f/∂y) = ∂/∂x(28y^6) = 0 (since we have no x terms in the derivative of ∂f/∂y)Since f_xy = f_yx = 0, we can say that f_xy = f_yx.

Therefore, the value of fx is 21x^6 and the value of fy is 28y^6. Hence, the value of fxy is 0 and fyx is also 0.

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The value of the integral is 15.87.

The given integral is:∫∫R 10(x+y) dAwhere R={(x,y)∣16≤x²+y²≤25,x≤0} in rectangular coordinates.In rectangular coordinates, the equation of circle is x²+y² = r², where r is the radius of the circle and the equation of the circle is given as: 16 ≤ x² + y² ≤ 25 ⇒ 4 ≤ r ≤ 5We need to evaluate the integral over the region R using rectangular coordinates and integrate first with respect to x and then with respect to y.∫∫R 10(x + y) dA = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy...[since x < 0]

Now, integrating ∫(x+y) dx we get ∫(x+y) dx = (x²/2 + xy)Therefore, 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) [ (x²/2 + xy) ] dy dx= 10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dxNow integrating with respect to y we get∫(x²/2 + xy) dy = (xy/2 + y²/2)

Putting the limits and integrating we get10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dx = 10∫ from 4 to 5 [(∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy)] dx = 10∫ from 4 to 5 [(x²/2)[y]^(-√(16-x²) )_(^(-√(25-x²))] + [(xy/2)[y]^(-√(16-x²) )_(^(-√(25-x²)))] dx = 10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dxNow integrating with respect to x, we get10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dx = [ (10/3) [(25/3)^(3/2) - (16/3)^(3/2)] - 5√3 - (5/3)[(25/3)^(3/2) - (16/3)^(3/2) ] ]Ans: The value of the integral is 15.87.

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The maximum value of the objective function Z is 120. The optimal values for the decision variables are X1 = 8, X2 = 0, and X3 = 0. The constraints are satisfied, and the optimal solution has been reached using the Simplex Method.

To compute the problem using the Simplex Method, let's convert it into standard form.

Maximize:

Z = 6X1 + 10X2 + 5X3

Subject to the constraints:

X1 + 2X2 + 4X3 <= 8

6X1 + 4X2 <= 24

6X1 + 5X3 <= 30

X1, X2, X3 >= 0

Introducing slack variables S1, S2, and S3 for each constraint, the constraints can be rewritten as equalities:

X1 + 2X2 + 4X3 + S1 = 8

6X1 + 4X2 + S2 = 24

6X1 + 5X3 + S3 = 30

Now, we have the following equations:

Objective function:

Z = 6X1 + 10X2 + 5X3 + 0S1 + 0S2 + 0S3

Constraints:

X1 + 2X2 + 4X3 + S1 = 8

6X1 + 4X2 + S2 = 24

6X1 + 5X3 + S3 = 30

X1, X2, X3, S1, S2, S3 >= 0

Next, we will create the initial simplex tableau:

  | X1 | X2 | X3 | S1 | S2 | S3 | RHS |

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

Z  | 6  | 10 | 5  | 0  | 0  | 0  | 0   |

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

S1 | 1  | 2  | 4  | 1  | 0  | 0  | 8   |

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

S2 | 6  | 4  | 0  | 0  | 1  | 0  | 24  |

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

S3 | 6  | 0  | 5  | 0  | 0  | 1  | 30  |

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

By performing the simplex pivot operations and iterating through the simplex method steps, we find the following tableau:

  | X1 | X2 | X3 | S1 | S2 | S3 | RHS |

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

Z  | 0  | 0  | 5  | -6 | 0  | -60| 120 |

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

X1 | 1  | 2  | 4  | 1  | 0  | 0  | 8   |

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

S2 | 0  | -8 | -24| -6 | 1  | 0  | 0   |

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

S3 | 0  | 0  | -1 | -6 | 0  | 1  | 0   |

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

The optimal solution is Z = 120, X1 = 8, X2 = 0, X3 = 0, S1 = 0, S2 = 0, S3 = 0.

Therefore, the maximum value of Z is 120, and the values of X1, X2, and X3 that maximize Z are 8, 0, and 0, respectively.

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