A bottle maker believes that 23% of his bottles are defective.If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%? Round your answer to four decimal places.

Answer:

Hope this helps! All you needed to do was add and subtract. Go through the slides, I added the step by step explanation, as well as the final table which contains the answers.

The value of the expressions are:

24(5/9) +30(7/9) = 6(2/9)

45(2/9) +39(3/9) = 84(5/9)

28.98 + (-52.22) =-23.24

56.75 + 75.12 = 131.87

We have,

Expressions:

-24(5/9) +30(7/9)

Simplifying the fractions.

This can be written as,

= (-24 + 30) +(-5/9 + 7/9)

= 6 + 2/9

= 6(2/9)

45(2/9) +39(3/9)

= (45 + 39) + (2/9 + 3/9)

= 84 + 5/9

= 84(5/9)

28.98 + (-52.22)

= 28.98 - 52.22

= -23.24

56.75 + 75.12

= 131.87

Thus,

The value of the expressions are:

24(5/9) +30(7/9) = 6(2/9)

45(2/9) +39(3/9) = 84(5/9)

28.98 + (-52.22) =-23.24

56.75 + 75.12 = 131.87

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Answer:2

Step-by-step explanation:

Answer:

x = -8, 1

Step-by-step explanation:

Hi there!

[tex]x^2+7x=8[/tex]

Move 8 to the other side:

[tex]x^2+7x-8=8-8\\x^2+7x-8=0[/tex]

Now, we can ask ourselves: what two factors of -8 add to 7? Those two numbers would be 8 and -1. Knowing this, factor:

[tex](x+8)(x-1)=0[/tex]

Because of the zero product property (that states that if the product of two numbers is 0, then one of the numbers must be equal to 0), we can find the solutions to the quadratic by setting each term equal to 0:

[tex]x+8=0\\x=-8[/tex]    

[tex]x-1=0\\x=1[/tex]

Therefore, the solutions of the quadratic are -8 and 1.

I hope this helps!

9514 1404 393

Answer:

  (a) The blue line ... solution ... (-6, -2)..

Step-by-step explanation:

The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.

The blue line represents the equation 2x -3y = -6.

The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.

9514 1404 393

Answer:

  14.3%

Step-by-step explanation:

We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.

The APR is about 14.3%.

_____

The amount to be repaid is calculated using the simple interest formula:

  A = P(1 +rt) = $4900(1 +0.08·4) = $6468

Then the required monthly payment (for 48 months) is ...

  $6468/48 = $134.75

__

The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...

  A = 4900(r/12)/(1 -(1 +r/12)^-48)

In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).

_____

Additional comment

The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.

We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.

Answer:

the answer to this question is equal to 162

Answer:

six in parenthesis n minus two

Step-by-step explanation:

2 ways could be:

A. N minus two then multiply by six

B. Six times parentheses n minus two end parentheses

Answer:

18.05

Step-by-step explanation:

Answer:

Use inequalities.

At certain x values.

Step-by-step explanation:

[tex]3 \leqslant x \leqslant 6[/tex]

[tex] - \infty < x < \infty [/tex]

[tex]x = 6[/tex]

Answer:

7 / 17 ;

10 / 17 ;

5 / 17

Step-by-step explanation:

Guests :

Mother = 1

Aunts = 3

Uncles = 3

Brothers = 4

Male cousin = 1

Female cousin = 5

_________________

Total guests = 17

Since each of the guests have an equal probability of arrival :

Probability that first guest to arrive :

Brother or uncle :

Number of brothers =4

Number of uncles = 3

P(brother or uncle) = required outcome / Total possible outcomes

Required outcome (number of brothers + uncles) = (4 + 3) = 7

Total possible outcomes = total guests = 17

P(brother or uncle) = 7 / 17

2.)

P(brother or cousin) :

Required outcome = (number of brothers + cousins) = (4 + 1 + 5) = 10

Total possible outcomes = total guests = 17

P(brother or cousin) = 10/17

3.)

P(brother or mother) ;

Required outcome = (number of brothers + mother) = (4+1) = 5

Total possible outcomes = total guests = 17

P(brother or mother) = required outcome / Total possible outcomes = 5 / 17

y=mx+b is the general formula of linear equation

y=-2x+5+3x+2

y=1x+7

m=1

b=7

Linear equation given in the question is,

2 + 3x + 5 - 2x = y

To simplify this equation further,

        (2 + 5) + (3x - 2x) = y

         7 + x = y

Now compare this linear equation with the slope-intercept form of the linear equation,

y = mx + b

Here, m = slope of the line'

b = y-intercept

By comparing the equations,

m = 1

b = 7

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Answer:

obtuse                    

aniuhafjhnfajfnha

Answer:

C)slides graph 4 units to the right

Answer:

[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]

Step-by-step explanation:

bxhrrrhi5u44ftj7gttjoy

Answer:

x = (y+1)/y

xy = (y+1)

xy -y = 1

y(x-1)=1

y = 1/(x-1)

Step-by-step explanation:

Answer:

104 square feet

Step-by-step explanation:

Total area of the wall: 10 x 16 = 160 square feet

Area of each window: 4 x 7 = 28

Since there are 2 windows, the total area that should not be painted is 28 x 2 = 56 square feet

160 - 56 = 104 square feet

To determine the area of the space to be painted on a wall with two rectangular windows, we need to calculate the total area of the wall and subtract the area of the windows.

First, let's calculate the area of the wall. The wall is 10 feet high and 16 feet wide, so the total area of the wall is: Area of wall = height × width = 10 feet × 16 feet = 160 square feet Next, let's calculate the area of each window. Each window is 4 feet high and 7 feet wide, so the area of each window is: Area of window [tex]= height × width = 4 feet × 7 feet = 28[/tex]  square feet Since there are two windows, the total area covered by the windows is 2 times the area of one window,

Which is: Total area of windows [tex]= 2 × 28[/tex] square feet = 56 square feet Finally, we can calculate the area of the space to be painted by subtracting the total area covered by the windows from the total area of the wall: Area to be painted = Area of wall - Total area of windows = 160 square feet - 56 square feet = 104 square feet Therefore, the area of the space to be painted on the wall is 104 square feet.

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Answer:

71

Step-by-step explanation:

The reference angle is always the smallest angle  with the x-axis.

The nearest x axis is at 0 or another name for 0 is 360

360 -289 = 71

The reference angle is 71

Answer:

A

Step-by-step explanation:

in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.

recall this formula :

(a-b)(a+b) = a^2 - b^2

in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of    3 -

after multiplying the denominator by its conjugate, we get:

(3 - [tex]\sqrt{6x}[/tex]) (3 +

at this point there is no need to solve the numerator as there is only one answer with this denominator.

hope this helps  :)

Answer:

Step-by-step explanation:

Answer:

∠ SPQ = 75°

Step-by-step explanation:

The sum of the 4 angles in a quadrilateral = 360°

Subtract the sum of the 3 angles from 360 for ∠ SPQ

∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°

Answer:

∠ CAB = 60°

Step-by-step explanation:

∠ CAD and ∠ BCA are alternate angles and congruent , so

∠ CAD = 30°

∠ BAD = 90° ( angle in a rectangle ) , then

∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°

The measure of the angle m∠CAB is 60.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

The rectangle has 90 degrees on all the vertices.

So,

In ΔABC,

The sum of the angles = 180

So,

30 + 90 + m∠CAB = 180

m∠CAB = 180 - 120

m∠CAB = 60

Thus,

The measure of the angle m∠CAB is 60.

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Answer:

The measure of ∠1 and ∠2 is 105° and 75° respectively

Step-by-step explanation:

In the given figure, line a is parallel to line b.

We need to find the measure of angles 1 and 2.

∠2 = 75° (because they form corresponding angles)

We know that, interior angles add up to 180. So,

∠1 +75 = 180

∠1 = 180-75

∠1 = 105°

So, the measure of ∠1 and ∠2 is 105° and 75° respectively.

Answer:

-5/8

Step-by-step explanation:

13/ -56   -x = 11/28

Add 13/56 to each side

13/ -56   + 13/56  -x = 11/28+ 13/56

-x = 11/28 + 13/56

Get a common denominator

-x = 11/28 *2/2 +13/56

-x = 22/56 + 13/56

-x = 35/56

Divide top and bottom by 7

-x = 5/8

Multiply both side by -1

x = -5/8

Answer:

512000

Step-by-step explanation:

l=80cm

v=l^3

=80^3

=512000cm^3

Answer:

[tex] = { \boxed{ \sf{ \frac{2}{3} }}} \: { \tt{feet/sec }}[/tex]

Answer:

2/3

Step-by-step explanation:

The basic formula is d = r * t. The units are important. Time is usually recorded as seconds. d can be feet or meters in standard form. The formula has to be rearranged to get r by itself.

r = d/ t

d = 20 feet

t = 30 seconds

r = 20 feet / 30 seconds

r = 20 ft/sec

Even though you are told not to enter the units, it is still important to recognize what they are.

Answer:

A. x<7

Step-by-step explanation:

The point at x=7 is an open circle, so the sign is <, not ≤

Answer:

8c

f(g(x)) = x^4 + 2x^3 - x

g(f(x)) =  x^4 + 2x^3 + 2x^2 - x

Step-by-step explanation:

f(x) = x^2 - x ; g(x) = x^2 + x

f(g(x)) = (x^2 + x)^2 - (x^2 + x)

f(g(x)) = (x^2 + x)^2 - x^2 - x

f(g(x)) = (x^2 + x)(x^2 + x) - x^2 - x

f(g(x)) = x^4 + x^3 + x^3 + x^2 - x^2 - x

f(g(x)) = x^4 + 2x^3 - x

g(f(x)) = (x^2 - x)^2 + x^2 - x

g(f(x)) = (x^2 + x)(x^2 + x) + x^2 - x

g(f(x)) = x^4 + x^3 + x^3 + x^2 + x^2 - x

g(f(x)) =  x^4 + 2x^3 + 2x^2 - x

9514 1404 393

Answer:

  (b) √65

Step-by-step explanation:

The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.

  |1 -8i| = √(1² +(-8)²) = √(1+64) = √65

Answer:

A)

Step-by-step explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Divide by y

kl/y = f/(p + n) + r/u              Subtract r/u from both sides

kl/y - r/u = f/(p + n)               Multiply both sides by (p + n)

(kl/y - r/u ) (p + n) = f            Divide by (kl/y - r/u)

p + n = f / (kl/y - r/u)             Subtract n from both sides

p  =  f / (kl/y - r/u)  - n

I think I'd leave this as the answer. I don't think you are expected to make it a 2 tier fraction.

Answer:

Step-by-step explanation: