if we select 4 young american men at random, what is the probability that they are all 68 inches or shorter (that is, each one of them is 68 inches or shorter)? enter your answer as a numerical value rounded to three decimal places (for ex., 0.111, no text).

Answer:

Ok I will help because i'm the nicest person you'll ever meet lol Ok anyway

there will be no step by step explanation

Direction variation:   and Not direction variation:

y= 3x

X= -1

and

Y= 4

now for the other one the non-direction---------------------> Y = (2/7)x

------------------------------------------------------------------------------> -0.5x = Y

------------------------------------------------------------------------------> Y= 2.2x + 7

TADA I'm finished and your welcome!!! :D

Answer:

2(x+5)

Step-by-step explanation:

New Simplex Tableau:

| Basis | x1 | x2

To use the simplex tableau method to solve the given linear programming problem, we need to convert it into standard form. The standard form includes non-negativity constraints and all inequalities as less than or equal to constraints. Let's rewrite the problem in standard form:

Maximize: Z = 2x1 + 5x2 + 4x3

Subject to:

x1 + x2 + 2x3 + x4 = 20

2x1 + x2 + x3 + x5 = 10

0x1 + x2 - x3 + x6 = 5

3x1 + 0x2 + 3x3 + x7 = 12

x1, x2, x3, x4, x5, x6, x7 ≥ 0

Now, let's construct the initial simplex tableau:

Basis x1 x2 x3 x4 x5 x6 x7 RHS

x4 1 1 2 1 0 0 0 20

x5 2 1 1 0 1 0 0 10

x6 0 1 -1 0 0 1 0 5

x7 3 0 3 0 0 0 1 12

Z -2 -5 -4 0 0 0 0 0

Next, we will perform iterations to find the optimal solution. The goal is to make the coefficients in the Z row non-negative. We will select the most negative coefficient as the pivot column and the smallest ratio of the RHS to the pivot column value as the pivot row.

Iteration 1:

Pivot Column: x2 (most negative coefficient)

Pivot Row: x6 (smallest ratio of RHS / pivot column value)

Perform row operations to make x6 a basic variable:

Row 3 = Row 3 / 1

Perform column operations to clear the pivot column:

Row 1 = Row 1 - 1 * Row 3

Row 2 = Row 2 - 1 * Row 3

Row 4 = Row 4 - 0 * Row 3

Row 5 = Row 5 + 5 * Row 3

New Simplex Tableau:

Basis x1 x2 x3 x4 x5 x6 x7 RHS

x4 1 0 3 1 0 0 0 15

x5 2 0 2 0 1 0 0 35

x2 0 1 -1 0 0 1 0 5

x7 3 0 3 0 0 0 1 12

Z -2 0 -3 0 0 5 0 20

Iteration 2:

Pivot Column: x3 (most negative coefficient)

Pivot Row: x4 (smallest ratio of RHS / pivot column value)

Perform row operations to make x4 a basic variable:

Row 1 = Row 1 - 3 * Row 4

Row 2 = Row 2 - 2 * Row 4

Row 3 = Row 3 - (-1) * Row 4

Row 5 = Row 5 - 3 * Row 4

Perform column operations to clear the pivot column:

Row 2 = Row 2 - 2 * Row 5

Row 1 = Row 1 - 3 * Row 5

Row 3 = Row 3 - (-1) * Row 5

Row 7 = Row 7 - 0 * Row 5

New Simplex Tableau:

| Basis | x1 | x2

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the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

We are given that Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange.

Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies and we are asked to find the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples.

To solve this problem, we will use the formula for mean and variance of a binomial distribution.

Mean or Expected Value E(X) = np

Variance V(X) = np(1-p)The formula for standard deviation is as follows;

Standard deviation of X, σ(X) = √np(1 - p)The number of orange candies in each sample of size 25 is expected to be:

For Dynamite Mints: np = 25 × 0.1 = 2.5For Holiday Mints: np = 25 × 0.45 = 11.25Therefore, the expected total number of orange candies in the two samples is: 2.5 + 11.25 = 13.75The variance for Dynamite Mints is:

V(X) = np(1 - p) = 25 × 0.1 × (1 - 0.1) = 2.25The variance for Holiday Mints is:

V(X) = np(1 - p) = 25 × 0.45 × (1 - 0.45) = 6.9375Therefore, the total variance for the two samples is:

V(X1 + X2) = V(X1) + V(X2) = 2.25 + 6.9375 = 9.1875The standard deviation for the two samples is:

σ(X1 + X2) = √V(X1 + X2) = √9.1875 = 3.033

So, the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

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Answer:

ill help

Step-by-step explanation:

Answer:

x = -2, 7

Step-by-step explanation:

1.Single out 6x^2 to x^2 by dividing 6 on both sides

= x^2-5x-14=0

2.Write -5x as a difference in order to factor

= x^2+2x-7x-14=0

3. Factor.

= (x+2)(x-7)

4. Set equal to 0

x+2=0

x=-2

x-7=0

x=7

The solution of the equation 6x² – 30x – 84 = 0 from least to greatest will be  –2 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

6x² – 30x – 84 = 0

Then the factor of the equation will be

        x² – 5x – 14 = 0

x² – 7x + 2x – 14 = 0

x(x – 7) + 2(x – 7) = 0

       (x + 2)(x – 7) = 0

Then the solution will be

x = –2, 7

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To find the values of x for which the two trinomials are equal, we need to set them equal to each other and solve for x.

For the trinomials 3x^2 - 4x + 3 and x^2 + x + 1:

3x^2 - 4x + 3 = x^2 + x + 1

By rearranging the equation and combining like terms, we get:

2x^2 - 5x + 2 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:

(2x - 1)(x - 2) = 0

Setting each factor equal to zero, we have:

2x - 1 = 0   -->   2x = 1   -->   x = 1/2

x - 2 = 0   -->   x = 2

Therefore, the values of x for which the two trinomials are equal are x = 1/2 and x = 2.

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Answer:

x = tan (3/4) therefore you cannot use (4/3)

Step-by-step explanation:

tan = opp over adj

Answer:

x = 32/3

Step-by-step explanation:

Step 1: Write equation

x/6 = 16/9

Step 2: Solve for x

The minimum amount of emergency savings you should have is $130.

To determine the minimum amount of emergency savings you should have, we need to consider the essential expenses.

In this case, the gasoline expense and the credit card payment are marked as essential expenses.

Let's calculate the minimum amount of emergency savings required to cover these essential expenses.

Essential expenses:

Gasoline (essential) = $100

Credit card payment (essential) = $30

To calculate the minimum emergency savings required, we add up the essential expenses:

Minimum emergency savings = Gasoline (essential) + Credit card payment (essential)

Minimum emergency savings = $100 + $30

Minimum emergency savings = $130

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Wayne's rectangular patio is adjacent to his house, and he wants to hang a string of lights around three sides of the patio, which is 86 feet long in total. The length of the patio, which is the side along the house, is 6 feet longer than twice its width. In this problem, we need to find the length and width of the patio.

Let's assume the width of the patio is 'w' feet. According to the given information, the length of the patio is 6 feet longer than twice its width, which can be expressed as 2w + 6 feet.

The total length of the three sides of the patio is given as 86 feet. Since we have two sides of equal length (width) and one side of length (length), we can set up the following equation:

2w + 6 + 2w + 2w = 86

Simplifying the equation, we have:

6w + 6 = 86

Subtracting 6 from both sides:

6w = 80

Dividing both sides by 6:

w = 80/6

w ≈ 13.33 feet (rounded to two decimal places)

Therefore, the width of the patio is approximately 13.33 feet. To find the length, we substitute the value of 'w' back into the equations for the length:

Length = 2w + 6

Length = 2(13.33) + 6

Length ≈ 32.67 feet (rounded to two decimal places)

Thus, the length of the patio is approximately 32.67 feet.

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Answer:

x=10

Step-by-step explanation:

8x+10=6x+30

8x-6x=30-10

2x=20

x=10

Answer:

225%

Step-by-step explanation:

250*.1 = 25

250-25=225$

Answer:

it's B

Step-by-step explanation:

14

Answer: B

11 - (-3) = 14.

-3 + 3 = 0.

11 + 3 = 14.

The answer is B, 14.

Hope it helps!

The solution of each of the quadratic equations are:

5) x = +3, -3

6) x = +3/2, -3/2

7) x = -4, 1/3

8) x = +9, -9

The general form of a quadratic equation is:

ax² + bx + c = 0

The quadratic formula to find the roots is:

x = [-b ± √(b² - 4ac)]/2a

5) The quadratic equation is given as 4x² - 36.

Thus:

x = [-0 ± √(0² - 4(4 * -36))]/2(4)

x = ±√4(4 * 36))/8

x = ±24/8

x = +3, -3

6) The quadratic equation is given as 64x² - 144

Thus:

x = [-0 ± √(0² - 4(64 * -144))]/2(64)

x = ±(√36864)/8

x = ±192/128

x = ±3/2

x = +3/2, -3/2

7) The quadratic equation is given as 3x² + 11x - 4

Thus:

x = [-11 ± √(11² - 4(3 * -4))]/2(3)

x = [-11 ± (√169)]/6

x = (-11 ± 13)/6

x = -4, 1/3

8) The quadratic equation is given as x² - 81

Thus:

x = [-0 ± √(0² - 4(1 * -81))]/2(1)

x = ±(√324)/2

x = ±18/2

x = ±9

x = +9, -9

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Answer:

5n + 3

Step-by-step explanation:

8 , 13 , 18

difference = 5

8 - 5(1) = 3

therefore nth term = 5n + 3

proof:

5(2) + 3 = 13

5(3) + 3 = 18

Step-by-step explanation:

Hey there!

The sequences are; 8,13,18,23.....

Common difference (d)= 5

Use formula: tn = t1+(n-1)d

Where d is the common difference and t1 is first sequence.

Or, tn = 8 + (n-1)5

= 8+5n -5

= 5n +3.

Therefore the required nth term is; tn = 5n+3.

Check;

1st term (t1) = 8 = 5×1+3=8 (true)

2nd term (t2) = 13 = 5×2+3=13 (true)

3rd term (t3)= 18 = 5×3+3=18 (true)

4th term (t4) = 23 = 5×4+3=23 (true).

Hope it helps..

Answer:

slope is -3

y-intercept is -2

Step-by-step explanation:

Answer:

y+2=5×

Step-by-step explanation:

because it is unlike term

Answer:

34

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A prime polynomial is simply an irreducible polynomial.

[tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

First, we test the options.

[tex]\mathbf{x + 9y^2}[/tex]

The above function cannot be reduced further.

Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

[tex]\mathbf{3m + 9n}[/tex]

Factor out 3

[tex]\mathbf{3(m + 3n)}[/tex]

[tex]\mathbf{3m + 9n}[/tex] is not a prime because it can be factored as [tex]\mathbf{3(m + 3n)}[/tex]

[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex]

Factor out x

[tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]

[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex] is not a prime because it can be factored as [tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]

Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

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Answer:

P(x) = (-0.2x² + 480x - 24480)

Step-by-step explanation:

1). Expression representing the "Cost" to produce the shirts is,

  C(x) = 160x + 24480

  Where 'x' represents the number of shirts.

  Cost to produce 900 printed shirts will be,

   C(900) = 160×900 + 24480

                = 144000 + 24480

                = Php 168480

2). Revenue generated by selling 900 shirts is,

   R(x) = 640x - 0.2x²

   For x = 900,

   R(x) = 640(900) - 0.2(900)²

          = 576000 - 162000

          = Php 414000

3). Expression for profit:

   Since, Profit = Revenue generated - Cost for production

   P(x) = R(x) - C(x)

          = (640x - 0.2x²) - (160x + 24480)

          = (640x - 160x) - 0.2x² - 24480

          = 480x - 0.2x² - 24480

  P(x) = (-0.2x² + 480x - 24480)

Sides of a square are all the same.

4(x-2) = (5x-20)

Distribute the left side:

4x -8 = 5x-20

Subtract 4x from both sides:

-8 = x -20

Add 20 to both sides:

X = 12

Now replace x with 12 and solve for the length:

5(12) -20 = 60-20 = 40

The sides are 40 cm long.

Answer:

Step-by-step explanation:

Solving for variables

1.......................................

2.......................................

3.......................................

4.......................................

here are your answer

d = 2/3

c = 3/2

y = 2/3

x = 4 2/19

have a good day

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

the answer is A.6(x + 3)

The two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16 are x = 5/6 and x = 17/6. Therefore, the correct option is B) 5/6, 25/6.

To find the two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16, we need to solve the equation for x.

Let's start by isolating the cosine term:

12cos(2π/5x) = 16 - 10

12cos(2π/5x) = 6

Next, divide both sides of the equation by 12:

cos(2π/5x) = 6/12

cos(2π/5x) = 1/2

To find the values of x that satisfy this equation, we can take the inverse cosine (arccos) of both sides:

2π/5x = arccos(1/2)

To determine the two smallest positive solutions, we need to find the values of x that correspond to the acute angles whose cosine is 1/2.

The arccosine of 1/2 is π/3, so:2π/5x = π/3

Next, solve for x:

x = (π/3)(5/2π)

x = 5/6

Therefore, the first solution for x is 5/6.

To find the second solution, we can add 2π to the right-hand side of the equation:

x = (π/3)(5/2π) + 2π

x = 5/6 + 12π/6

x = 5/6 + 2

x = 5/6 + 12/6

x = 17/6

Therefore, the second solution for x is 17/6.

Option b

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Answer:

X=3

Step-by-step explanation:

The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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Answer:

[tex]-3x+y=10[/tex]

Step-by-step explanation:

To write this equation we first need to know what the standard form is. Standard form of a line is written as [tex]Ax + By = C[/tex]. To get this, we first need to put the equation into point slope form or [tex]y-y1 = m(x-x1)[/tex] where [tex]m[/tex] is slope and [tex](x1,y1)[/tex] is a point on the graph. Using the information we know we can make the equation [tex]y+2=4(x+3)[/tex].

Now that we have point slope form we need to convert it. To do this we need to first get rid of the parenthesis by distribution. This will give us [tex]y+2=3x+12[/tex]

Next, we know we need to get [tex]x[/tex] and [tex]y[/tex] on the same side of the equal sign. We do this by subtracting 3x on both sides to get [tex]-3x+y+2=12[/tex]

Finally, we can subtract 2 on both sides to put the equation into standard form. This will give us [tex]-3x+y=10[/tex]