Prove The Following
------------------------------

The binomial distribution assumes that each sample is independent and the probability of success remains constant throughout the sampling process.

To solve these probability questions, we can use the binomial distribution formula. Let's define the following variables:

p = Probability of preferring a permanent, full-time job = 0.67

n = Sample size = 100

a. To find the probability that fewer than 71% prefer a permanent, full-time job, we need to calculate the cumulative probability from 0% to 70% (0.71):

P(X < 0.71 * 100) = P(X < 71) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 0 to 70

b. To find the probability that between 61% and 71% prefer a permanent, full-time job, we need to calculate the cumulative probability from 60% (0.6) to 70% (0.71):

P(0.6 * 100 ≤ X ≤ 0.71 * 100) = P(60 ≤ X ≤ 71) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 60 to 71

c. To find the probability that more than 69% prefer a permanent, full-time job, we need to calculate the cumulative probability from 70% (0.7) to 100% (1):

P(X > 0.7 * 100) = P(X > 70) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 71 to 100

d. If a sample of 400 is taken, the only change is the value of n. We will use n = 400 to recalculate the probabilities in (a), (b), and (c) using the same formulas.

Note: The binomial distribution assumes that each sample is independent and the probability of success remains constant throughout the sampling process.

Please note that calculating these probabilities requires performing multiple calculations and it would be more suitable to use statistical software or a calculator with binomial distribution capabilities to obtain the precise results.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

Answer:

Step-by-step explanation:

Given the following :

Number of shares purchased (2016) = 50

Purchase price of shares $396.33 per share

Closing price per share four years later = $778.38

A) What did Chadwick pay for all of the shares in 2016?

Purchase price per share × number of shares.

$396.33 × 50 = $19,816.50

B) What was the closing value of all of the shares four years later?

Closing price per share × number of ahaf

=$778.38 × 50

= $38,919

C.) Profit on stock :

$(38,919 - 19,816.50)

= $19,102.5

D) What is his rate of return on his shares when he sold them?

(Current Purchase - initial value) /current price

(778.3 - 396.33) / 396.33

= (381.97 / 396.33) 100%

= 0.9637675

=

The equation of the circle in this problem is given as follows:

(x - 2)² + (y + 4)² = 36.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The coordinates of the center of the circle are given as follows:

(2, -4).

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence, considering the horizontal line from the center to point (8, -4), it's measure is given as follows:

r = 6.

Thus the equation is:

(x - 2)² + (y + 4)² = 36.

More can be learned about the equation of a circle at https://brainly.com/question/1506955

#SPJ1

Answer:

The angular position of the minute hand at 3:30 is 2π radians.

Step-by-step explanation:

In a clock, the minute hand completes one full revolution (360 degrees) in 60 minutes or 2π radians.

At 3:30, the minute hand is at the 6 o'clock position, which corresponds to 180 degrees or π radians.

Since 3:30 is halfway between the 3 and 4 on the clock, the minute hand has moved halfway between the 6 o'clock position and the 12 o'clock position.

Therefore, the angular position of the minute hand at 3:30 is:

θ = π + (1/2) * (2π) = π + π = 2π radians.

Hence, the angular position of the minute hand at 3:30 is 2π radians.

#SPJ11

Answer:

d

Step-by-step explanation:

you are adding 22 dollars each month and 125 is your starting balance

The equation shows your balance, b, in m months will be b( m) = $125 + $22 m.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

Savings account balance = $125

Money added per month = $22

The obtained equation is,

b( m) = $125 + $22 m.

Thus, the equation shows your balance, b, in m months will be b( m) = $125 + $22 m.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

The  value of x in the given right triangle is determined as 1.36.

The value of x is calculated by applying trig ratios as follows;

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of x is calculated as follows;

tan (23) = opposite side / hypothenuse side

tan (23) = x / 3.2

x = 3.2 x tan (23)

x = 1.36

Thus, the  value of x is determined by applying trigonometry ratios.

Learn more about trig ratio here: brainly.com/question/10417664

#SPJ1

For the first equation y' = (2 + y)y - x on [0, 1] with y(0) = 0 and h = 0.2, and the second equation y' = y sin(x) on [0, 7] with y(0) = 1 and h = 4

The given problem consists of two separate differential equations. In the first equation, y' = (2 + y)y - x on the interval [0, 1], with an initial condition of y(0) = 0 and a step size of h = 0.2. In the second equation, y' = y sin(x) on the interval [0, 7], with an initial condition of y(0) = 1 and a step size of h = 4.

For the first equation, we can solve it using numerical methods such as Euler's method or Runge-Kutta methods. By applying Euler's method with the given step size, we can approximate the values of y at different points within the interval [0, 1].

Starting with the initial condition y(0) = 0, we can calculate the values of y at subsequent points using the formula y_i+1 = y_i + h*f(x_i, y_i), where f(x, y) = (2 + y)y - x represents the given differential equation. By repeating this process for each step, we can generate an approximation of the solution y(x) within the specified interval.

For the second equation, y' = y sin(x), we can also use numerical methods such as Euler's method or Runge-Kutta methods. Similarly, by applying Euler's method with the given step size, we can approximate the values of y at different points within the interval [0, 7]. Starting with the initial condition y(0) = 1, we can calculate the values of y at subsequent points using the formula y_i+1 = y_i + h*f(x_i, y_i), where f(x, y) = y sin(x) represents the given differential equation. By repeating this process for each step, we can generate an approximation of the solution y(x) within the specified interval.

In summary, for the first equation y' = (2 + y)y - x on [0, 1] with y(0) = 0 and h = 0.2, and the second equation y' = y sin(x) on [0, 7] with y(0) = 1 and h = 4, we can use numerical methods like Euler's method to approximate the solutions of the differential equations within the respective intervals.

Learn more about Differential Equations here:

brainly.com/question/32645495

#SPJ11

A)after 5 years without any extra deposit, we expect to have $36,603.86 in the account. B) we will have $79,998.77 in the account after 5 years. C)  the smallest value of D to be greater than $50,000 in 5 years would be $3,800.28.

a) The formula to calculate the compound interest is given as:A=P(1+r/n)^(nt)

Here,P = Principal (initial amount) = $30,000r = Yearly Interest Rate = 4% or 0.04n = number of times the interest is compounded per year = ∞t = time (in years) = 5 yearsSo, using the above values, we get:A = 30,000(e)^(0.04×5) = $36,603.86

Thus, after 5 years without any extra deposit, we expect to have $36,603.86 in the account.

b) Now suppose you make constant yearly deposits of $2,000. Write down an IVP that models this problem, find its solution and estimate how much money we will have in the account after 5 years.

The given amount is deposited every year, hence we have:the principal amount, P = $30,000the yearly amount added, a = $2,000Yearly interest rate, r = 4% or 0.04Number of times the interest is compounded per year, n = ∞t = 5 yearsThe general formula is: y = Ce^(kt) + (a/k) (e^(kt) - 1), where y is the total amount in the account, C is the initial amount, k is the interest rate, a is the yearly amount added, and t is the number of years.

The Initial Value Problem (IVP) is:y(0) = 30000Given, y(0) = 30000We can obtain k by differentiating the given function with respect to t to obtain:dy/dt = ky + a, with initial condition y(0) = 30000Differentiating once again gives:d^2y/dt^2 = k(dy/dt) = k(ky+a)Substituting k = 0.04, a = 2000, and y(0) = 30000 we have:y(0) = C = 30000

Using the above differential equations, we obtain:k = 0.04Then,y(t) = Ce^(0.04t) + (2000/0.04) (e^(0.04t) - 1)y(t) = 30000e^(0.04t) + 50000.00 (e^(0.04t) - 1)After 5 years, y(5) = 30000e^(0.04×5) + 50000.00 (e^(0.04×5) - 1)y(5) = $79,998.77

Thus, we will have $79,998.77 in the account after 5 years.

c) Now suppose you are willing to increase the amount you deposit every year, calling this new fixed amount D.

Let the yearly amount be D. The principal amount is P = $30,000. Yearly interest rate, r = 4% or 0.04. Number of times the interest is compounded per year, n = ∞ and t = 5 years.

So, we can use the formula y = P(e)^(rt) + D[(e)^(rt) - 1]/rto calculate the future value with yearly deposits of D dollars. We want the future value to be greater than $50,000.

Therefore, the equation we need to solve is:30,000e^(0.04×5) + D[(e)^(0.04×5) - 1]/0.04 > 50,000Solving the above equation, we get:D > 3,800.28

Therefore, the smallest value of D to be greater than $50,000 in 5 years would be $3,800.28.

Know more about Initial Value Problem here,

https://brainly.com/question/30466257

#SPJ11

Euclid's Proposition III.22 states that if ABCD is a quadrilateral inscribed in a circle, then the sum of the measures of the opposite angles is 180°. This can be proved by considering the properties of inscribed angles and arcs.

Let ABCD be a quadrilateral inscribed in a circle with center O. We want to prove that μ(LABC) + μ(LCDA) = 180° and µ(LBCD) + µ(LDAB) = 180°.

First, consider angle LABC. This angle intercepts the arc CD. According to the inscribed angle theorem, the measure of angle LABC is equal to half the measure of the intercepted arc CD. Similarly, angle LCDA intercepts the arc AB, so μ(LCDA) = 1/2 × μ(arc AB).

Since the sum of the measures of the arcs of a circle is 360°, we have μ(arc AB) + μ(arc CD) = 360°. Therefore, 1/2 × μ(arc AB) + 1/2 × μ(arc CD) = 1/2 × 360°, which simplifies to μ(LCDA) + μ(LABC) = 180°.

Similarly, by applying the same reasoning, we can show that μ(LBCD) + μ(LDAB) = 180°.

Hence, we have proved Euclid's Proposition III.22, which states that if ABCD is a quadrilateral inscribed in a circle, then the sum of the measures of the opposite angles is 180°.

Learn more about quadrilateral here:

https://brainly.com/question/29934440

#SPJ11

Answer:

3x-9+4x+3=7x-6=29

7x=35

x=5

Step-by-step explanation:

The absolute maximum value of f(x, y) on D is 0, and the absolute minimum value is -64.

(a) To find the critical points of the function f(x, y) = 4xy^2 - x^2y^2 - xy^3, we need to find the values of x and y where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x:

∂f/∂x = 4y^2 - 2xy^2 - y^3

Taking the partial derivative with respect to y:

∂f/∂y = 8xy - 2x^2y - 3xy^2

Setting both partial derivatives equal to zero and solving the resulting system of equations will give us the critical points.

4y^2 - 2xy^2 - y^3 = 0   ...(1)

8xy - 2x^2y - 3xy^2 = 0   ...(2)

From equation (1), we can factor out y^2:

y^2(4 - 2x - y) = 0

This gives us two possibilities: y = 0 or 4 - 2x - y = 0, which simplifies to y = 4 - 2x.

Substituting y = 0 into equation (2), we get:

8xy = 0

This implies that either x = 0 or y = 0.

So, we have three possible cases for the critical points:

Case 1: y = 0, which implies x = 0 from equation (2).

Case 2: x = 0, which implies y = 4 from the equation y = 4 - 2x.

Case 3: Solving the equations 4 - 2x - y = 0 and 8xy - 2x^2y - 3xy^2 = 0 simultaneously will give us additional critical points.

(b) To find the absolute maximum and minimum values of f(x, y) on the closed triangular region D, we need to evaluate the function at the vertices of the triangle and at the critical points found in part (a).

The vertices of the triangle D are (0, 0), (0, 6), and (6, 0).

Evaluate f(x, y) at the vertices:

f(0, 0) = 0

f(0, 6) = 0 - 0 - 0 = 0

f(6, 0) = 4(6)(0)^2 - (6)^2(0)^2 - (6)(0)^3 = 0

Evaluate f(x, y) at the critical points:

f(0, 0) = 0

f(0, 4) = 4(0)(4)^2 - (0)^2(4)^2 - (0)(4)^3 = -64

f(2, 2) = 4(2)(2)^2 - (2)^2(2)^2 - (2)(2)^3 = 8 - 8 - 16 = -16

Therefore, the absolute maximum value of f(x, y) on D is 0, and the absolute minimum value is -64.

Learn more about critical points and finding extrema of functions here:

https://brainly.com/question/31339061

#SPJ11

Answer:

P(both soccer and basketball) = [tex]\frac{18}{31}[/tex]

Step-by-step explanation:

Let B, S denote number of students who play basketball and soccer.

As 31 play basketball, 59 play soccer and 18 of the students play both basketball and soccer,

[tex]n(B)=21\\n(S)=59[/tex]

n(B∩S) = 18

To find P (Soccer |Basketball) that is P(S∩B),

use P(S∩B) = P(both soccer and basketball)/ P(B)

P(both soccer and basketball) = Number of students who play both soccer and basketball / Total number of students

= [tex]\frac{18}{145}[/tex]

Also,

P(B) = Number of students who play basketball / Total number of students

= [tex]\frac{31}{145}[/tex]

So,

P(S∩B) = [tex]\frac{\frac{18}{145} }{\frac{31}{145} }=\frac{18}{31}[/tex]

That is

P(both soccer and basketball) = [tex]\frac{18}{31}[/tex]

The choice of a and α that minimizes the variance of β, subject to the condition of unbiasedness, is given by α =

σ(X2)^2/[σ(X1)^2 + σ(X2)^2] and β = σ(X1)^2/[σ(X1)^2 + σ(X2)^2].

The estimators X1 and X2 with their standard errors were used to independently conduct two surveys to estimate a

population mean μ. Denote the estimators and their standard errors by X_1 X_2 and sigma X_1 and sigma X_2.

Assume that X_1 and X_2 are unbiased, and they can be combined to give a better estimator X = αX1 + βX2 for some α

and β.The conditions on α and β that make the combined estimator X unbiased are obtained as follows: Expectation of

X = E(X) = E(αX1 + βX2)E(X) = αE(X1) + βE(X2)Since X1 and X2 are unbiased, E(X1) = μ and E(X2) = μThus, E(X) = αμ + βμ =

μα + μβSolving for α, we have α + β = 1 α = 1 - βThis implies that the unbiased estimator X is given by X = (1 - β)X1 + βX2.

The variance of X can be found as follows: Var(X) = Var[(1 - β)X1 + βX2]Since X1 and X2 are independent, we have

Var(X) = [(1 - β)^2 Var(X1)] + [β^2 Var(X2)]Var(X) = (1 - β)^2 σ(X1)^2 + β^2 σ(X2)^2Since we need to find the values of α and

β that minimize Var(X), we need to differentiate Var(X) with respect to β and equate it to zero. Hence, d[Var(X)]/dβ = 2(1

- β)σ(X1)^2 - 2βσ(X2)^2 = 0On solving for β, we haveβ = σ(X1)^2/[σ(X1)^2 + σ(X2)^2]Thus, α = 1 - β = σ(X2)^2/[σ(X1)^2 +

σ(X2)^2]Therefore, the choice of a and α that minimizes the variance of β, subject to the condition of unbiasedness, is

given by α = σ(X2)^2/[σ(X1)^2 + σ(X2)^2] and β = σ(X1)^2/[σ(X1)^2 + σ(X2)^2].

Learn more about variance:https://brainly.com/question/9304306

#SPJ11

Answer:

Step-by-step explanation:

a(b+c) = (ab)+(ac)

by property of distribution

a(b+c) = ab + ac

Answer:

8.72 • 10^7

Step-by-step explanation:

Answer:

Median

Step-by-step explanation:

Because it divides line B into a prefect section

Answer:

a) 64

b) 9

c) 1

d) 49

Step-by-step explanation:

8^2 = 64

same as 8*8

1^2 = 1

same as 1*1

3^2 = 9

same as 3*3

7^2 = 49

same as 7*7

a: 64, b:9, c:1, d:49

Step-by-step explanation:

because 8 squared is 64, 3 squared is 9(3×3=9), 1 squared is 1(1×1), and 7 squared is 49.

Answer:

Answer is long, so Ill put it in the explanation.

Step-by-step explanation:

Domain: -∞ ≤ x ≤ ∞ (x goes infinitely in both directions)

Range: -∞ ≤ y ≤ 1 (infinite number of negative points, or going down, but stops at positive 1 going up)

y intercept: (0,0) (where the function meets the y-axis)

x-intercepts: (0,0) and (4,0) (where the function meets the x-axis)

minimum: -∞ ( doesnt have a lowest point, essentially there isnt one)

maximum: y = 1 (this is the highest point of the function)

f(6) = -3 (this is asking: when x = 6, what does y equal?)

This parabola is decreasing (it opens downwards)

Answer:

x^3+8

Step-by-step explanation:

used an online calculator lol

Answer:

-5.5

Step-by-step explanation:

Answer:

-5.5

Step-by-step explanation:

-54/8  

-5 first just put the whole number because that won't change

4/8 simplified is 1/2

1/2 as a decimal is 0.5

your answer is -5.5

Answer:

c = [tex]\frac{25}{4}[/tex]

Step-by-step explanation:

To make a perfect square

add ( half the coefficient of the x- term )² to x² + 5x

x² + 5x + ([tex]\frac{5}{2}[/tex] )²

= x² + 5x + [tex]\frac{25}{4}[/tex]

= (x + [tex]\frac{5}{2}[/tex] )² ← a perfect square

Answer:

I'm afraid that you cannot simplify this anymore.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

4.9/0.7=7

Answer:

yes

Step-by-step explanation:

A proportional equation is of the form

y = kx where k is the constant of proportionality

y = 150x is proportional

Step-by-step explanation:

Yes this is actually correct, labelling numbers gives it a meaning, and also makes it understandable to whoever is reading or solving a problem associated with the number

12+2=3 ordinarily would be false because

12+2=14

but when a label is attached

that is  12 inches + 2 feet= 3 feet

12 inches is  the same as 1 foot

so 1foot+2feet= 3 feet  

9 + 6 = 3 ordinarily is false as 9 + 6 = 15

but

√9feet + 6feet = 3yard  

3feet + 6feet = 3yard  

a. Sylvia can buy a maximum of 6 movie tickets in a week.

b. Sylvia can buy a maximum of 2 pizzas in a week.

c. Sylvia can buy 6 movie tickets with her budget, the opportunity cost of purchasing a pizza is 6 movie tickets.

a. To find the maximum number of movie tickets Sylvia can buy in a week, we need to divide her weekly budget by the price of each ticket.

Number of movie tickets = Weekly budget / Price of a movie ticket

Number of movie tickets = $24 / $4

Number of movie tickets = 6

Sylvia can buy a maximum of 6 movie tickets in a week.

b. To find the maximum number of pizzas Sylvia can buy in a week, we need to divide her weekly budget by the price of each pizza.

Number of pizzas = Weekly budget / Price of a pizza

Number of pizzas = $24 / $12

Number of pizzas = 2

Sylvia can buy a maximum of 2 pizzas in a week.

c. The opportunity cost of purchasing a pizza refers to the value of the next best alternative that Sylvia gives up when choosing to buy a pizza. In this case, since Sylvia has a fixed budget, the opportunity cost of purchasing a pizza would be the number of movie tickets she could have bought instead.

Since Sylvia can buy 6 movie tickets with her budget, the opportunity cost of purchasing a pizza is 6 movie tickets.

Learn more about budget from

https://brainly.com/question/29028797

#SPJ11

Answer:

20 points

Step-by-step explanation:

First you add 30 + 15, which equals 45.

Then, you subtract 25 from 45, (45-25) which equals 20

Answer: I don't understand your question

Step-by-step explanation:

my explanation is at the top

Answer:

Kindly check explanation

Step-by-step explanation:

Give the steps used in solving the equation :

4x - (x + 2) + 6 = 2 ( 3x + 8)

Step 1:

4 x - x + 2 + 6 = 6 x + 16

Step 2:

3 x + 8 = 6 x + 16

Step 3:

8 - 16 = 6x - 3x

Step 4:

- 8 = 3 x

Step 5:

- 8 / 3 = x

Jorge's error was made in STEP 1:

4x - (x + 2) + 6 = 2 ( 3x + 8)

OPENING THE BRACKET SHOULD GIVE :

4x-x-2 +6 = 6x+16 AND NOT 4x - x+2+6 = 6x+ 16

Hence,

4x - x - 2 + 6 = 6x+16

3x + 4 = 6x + 16

4 - 16 = 6x - 3x

- 12 = 3x

-12 / 3 = x

-4 = x

Answer:

Jorge distributed incorrectly.

Step-by-step explanation: