Of the cartons produced by a​ company, ​% have a​ puncture, ​% have a smashed​ corner, and ​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing​%. ​(Type an integer or a decimal. Do not​ round.)

Answer: (a) When he turns 68 , the account will have = $1,179,415.39

(b) $ 288,000

Step-by-step explanation:

Formula: Future value of annuity =[tex]P[\dfrac{(1+r)^n-1}{r}][/tex], where P+ periodic payment, r = rate of interest per period, n= number of periods.

As per given, we have

P= $1800

rate of interest = 6% = 0.06

(a) n= 68-28 = 40

Rate per period : r= [tex]\dfrac{0.06}{4}=0.015[/tex]  

Number of periods: n = 4x 40 =160

Now, Future value of amount when Mr. Pink turns 28 years = [tex]1800(\dfrac{(1+0.015)^{160}-1}{0.015})[/tex]

[tex]=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\$1179415.39[/tex]

Hence, when he turns 68 , the account will have = $1,179,415.39

(b) Total contribution = P × n

=1800 × 160

=$ 288,000

Hence, Total contribution =$ 288,000

Answer:

  φ ≈ 1.19029 radians   (≈ 68.2°)

Step-by-step explanation:

There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.

We want to compare ...

  y(t) = Asin(ωt +φ)

to

  y(t) = Psin(ωt) +Qcos(ωt)

Using trig identities to expand the first equation, we have ...

  y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Matching coefficients with the second equation, we have ...

  P = Acos(φ)

  Q = Asin(φ)

The ratio of these eliminates A and gives a relation for φ:

  Q/P = sin(φ)/cos(φ)

  Q/P = tan(φ)

  φ = arctan(Q/P) . . . . taking quadrant into account

__

We can also use our equations for P and Q to find A:

  P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²

  A = √(P² +Q²)

_____

Here, we want φ.

  φ = arctan(Q/P) = arctan(5/2)

  φ ≈ 1.19029 . . . radians

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Answer:

The width of the model will be  2.5 inches

Step-by-step explanation:

The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.

Step One: Determine the scale factor from the tower height.

The scale factor is obtained from the formula:

Scale factor = model size / observed size

This will be

Height of model tower/ height of the real tower.

The height of the model tower is 5 inches which is the same as 0.416667 ft

Scale factor = 0.416667 ft/ 40ft = 0.0104

Step two:  Multiply the width of the real-life tower by the scale factor to get the model width.

Width of model =20ft X 0.0104 = 0.208ft

Step three:  Convert your answer back to inches.

We will now have to convert 0.208 ft back to inches by multiplying by 12

This will be 0.208 X 12 =2.5 inches.

The width of the model will be  2.5 inches

Answer:

A. Cone

D. Rectangular Prism

E. Cylinder

F. Sphere

Step-by-step explanation:

Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.

Answer:

Step-by-step explanation:

Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;

Sn = a(1-rⁿ)/1-r  for r less than 1

r is the common ratio

n is the number of terms

a is the first term of the series

In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]

common ratio = (1/10)/(1/2) =  (1/50)/(1/10) =  (1/250)/(1/50) = 1/5  

a = 1/2

Substituting the given values into the equation above

S7 = 1/2{1 - (1/5)⁷}/1 - 1/5

S7 = 1/2(1- 1/78125)/(4/5)

S7 = 1/2 (78124/78125)/(4/5)

S7 = 78124/156,250 * 5/4

S7 = 390,620/625000

S7 = 39062/62,500

Hence the geometric sum is 39062/62,500

Answer:

[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]

Step-by-step explanation:

Hello,

I assume that you want to solve this system of two equations

   (1) 5x - y  = -7

   (2) 4x + 2y = -14

We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y

2*(1)+(2) gives

   10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28

   <=>

   14x = - 28 we can divide by 14 both parts

   x = -28/14 = -2

and then we replace x in (1)

   5*(-2)-y=-7

   -10-y=-7 add 7

   -10-y+7=0

   -3-y=0 add y

   -3 = y

which is equivalent to y = -3

do not hesitate if you have any question

Answer:

x = -2, y = -3

Step-by-step explanation:

5x - y = -7

4x + 2y = – 14

Multiply the first equation by 2

2(5x - y) = 2*-7

10x -2y = -14

Add this to the second equation to eliminate y

10x -2y = -14

4x + 2y = – 14

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

14x = -28

Divide by 14

14x/14 = -28/14

x = -2

Now find y

4x+2y = -14

4*-2 +2y = -14

-8+2y = -14

Add 8 to each side

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

Answer:

A= 66.6667

B = 333.3333

Step-by-step explanation:

Initial value of A = $20

Initial value of B = $80

Initial total=$ 28000

A moves up 50%= 20+(0.5*20)

A moves up 50% = 20+10

A moves up 50% =$ 30

B double it values = $80*2

B double it values = $160

Now total value is = $54000

A20+B80= 28000... equation 1

A30+B160= 54000.... equation 2

Multiplying equation 1 * 2

Multiplying equation 2 * 1

A40 +B160 = 56000

A30+B160= 54000

A30 = 2000

A= 2000/30

A= 200/3

A= 66.6667

A20+B80= 28000

Substituting A

200/3 (20) +B80= 28000

B80= 28000-4000/3

B80= 80000/3

B= 80000/240

B = 333.3333

Answer:

  C. g(-13) = 20

Step-by-step explanation:

Let's check the offered statements:

  A. g(0) = 2 . . . . . . doesn't match g(0) = -2

  B. g(7) = -1 . . . . . . 7 is not in the domain of g

  C. g(-13) = 20 . . . could be true

  D. g(-4) = -11 . . . . -11 is not in the range of g

Answer:

b = 4

Step-by-step explanation:

3 - b = 6 - 7

3 - b = -1

-b = -1 -3

-b = -4

b = 4

Complete question is;

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:

2005 Season: 73 77 78 76 74 72 74 76

2006 Season: 70 69 74 76 84 79 70 78

​A) Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.

B) What is the primary difference in performance between 2005 and 2006? What improvement,

if any, can be seen in the 2006 scores?

Answer:

A) 2006 mean = 75

2005 mean = 75

2006 standard deviation = 5.2644

2005 standard deviation = 2.0702

B)The primary difference is that variation is higher in the 2006 season than the 2005 season.

Step-by-step explanation:

A) Mean is the sum of all scores divided by the number of scores.

Thus;

μ_2005 = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8 = 75

Similarly;

μ_2006 = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8 = 75

Now, variance is calculated by the sum of the square of mean deviations divided by (n - 1)

Thus;

2005 Variance = ((73-75)² + (77-75)² + (78-75)² + (76-75)² + (74-75)² + (72-75)² + (74-75)² + (76-75)²)/(8-1) = 4.2857

2006 Variance = ((70-75)² + (69-75)² + (74-75)² + (76-75)² + (84-75)² + (79-75)² + (70-75)² + (78-75)²)/(8 - 1) = 27.7143

Now, standard deviation is the square root of variance.

Thus;

2005 standard deviation = √4.2857 = 2.0702

2006 standard deviation = √27.7143 = 5.2644

B) The primary difference is that variation is higher in the 2006 season than the 2005 season.

Also,

Answer:

1st blank: X axis reflection

2nd blank: Y axis reflection

Step-by-step explanation:

If you drew the first triangle and then the second triangle on a piece of paper, you would notice that it would reflect across the corresponding axis.

So the solution is to just draw it out.

Answer:

reflection across the x axis and the second is a reflection across the y axis.

Answer:

Optimal production = 600 gold pens

Revenue  = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000  ....................(1)   bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800  ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder)  .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4).  Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7)    [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x   [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue  = 600*7 = 4200 gold pens

Answer:

50% of 100<75% of 104

50% of 100>75% of 60

Step-by-step explanation:

For the inequality to support the statement, we can use 50% of 100 which is 50

Now we need to find "any other number" that is greater. I'll use 104 since it divides evenly. 75% of 104 is 78, 50<78

Now for the second one, we can use 50% of 100 again which is 50.

This time we need to find another number that is less than. I'll use 60. 75% of 60 is 45. 50>45

Answer:

4:00 pm

Step-by-step explanation:

To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.

5:30 minus 1 hour is 4:30.

Now, subtract 30 minutes.

4:30 minus 30 minutes is 4:00.

Malik started working on his English essay at 4:00 pm.

Hope that helps.

Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

To make it easier, you can convert 7/20 to a decimal, and as a decimal it is 0.35. 0.42*0.35=0.147, so .42*7/20=0.147.

Answer:

0.147

Step-by-step explanation:

0.42 * 7/20

Well, 0.42 = 42/100. Now we have both numbers as fractions.

We can simplify 42/100 to 21/50

Therefore we have 7/20 * 21/50

To multiply fractions multiply the numerators together and multiply the denominators together.

This gives: 147 / 1000

Which is equal to 0.147

Therefore 0.42 * 7/20 = 0.147

Answer:

  0

Step-by-step explanation:

The determinant of this matrix is zero (0).

Answer:  438.5L = 438000ml

Step-by-step explanation:

Answer:

Hey there!

An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.

Thus, the perimeter for this equilateral triangle would be 3(12)=36

Hope this helps :)

Answer:

[tex]\boxed{Perimeter = 36 \ units}[/tex]

Step-by-step explanation:

Perimeter = sum of all sides

Perimeter = 12 +12 + 12

Perimeter = 36 units

Answer:

(1400)(1+0.029/12)3(1+0.221/12)9

Step-by-step explanation:

A p e x

Answer:

Step-by-step explanation:

Just so you know how it looks on the page

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Answer:

The scores are equal

Step-by-step explanation:

The z-score for any normal distribution is:

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

(i) Score (X) = 40

Mean (μ)= 50

Standard deviation (σ) = 10

[tex]z=\frac{40-50}{10}\\ z=-1[/tex]

(ii) Score (X) = 45

Mean (μ)= 50

Standard deviation (σ) = 5

[tex]z=\frac{45-50}{5}\\ z=-1[/tex]

Both scores have the same z-score, which means that, relative to their respective distributions, the scores are equal.

Answer:

pleasse elaborate more

Step-by-step explanation:

Answer:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]

[tex](f/g)(2)=-4[/tex]

Step-by-step explanation:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]  and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]

Answer:

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all, let's find the factors of these two numbers and I will put in boxes the common factors.

[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]

The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The value of  annuity is [tex]P_v = \$ 32058[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 1500[/tex]

     The  interest rate  is   [tex]r = 8\% = 0.08[/tex]

     Frequency at which it occurs in a year is  n = 2 (semi-annually )

      The number of years is  [tex]t = 22 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)

 substituting values

             [tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]

             [tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]

             [tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]

            [tex]P_v = \$ 32058[/tex]

Answer:

Simply plug in the polynomial into a graphing calc.

Step-by-step explanation: