Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 6%? Round your answer to four decimal places.

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

Given,

When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;

Here,

25 × 45 = 1125

Now,

This is simply multiplicity;

1. 20 x 40: 20 x 5: 40 x 5

800 ; 100 ; 200

1100

This is not the problem.

2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5

800 ; 200 ; 100 ; 25

1125

This is the problem

3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5

800 ; 100 ; 100 ; 25

1025

This is not the problem

4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5

400 ; 1600 ; 100 ; 25

2125

This is not the problem

Therefore,

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

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The partial fraction of the compound fraction [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] is  [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions.

When fractions become too cumbersome to solve we split them into simpler units called partial fractions so that mathematical operations can easily be carried out on them.

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] can be split into the form, [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

where A and B are constants.

so,

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  =   [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

taking the LCM of the denominators of the split fractions, we have

(x-3)(x-5)

multiply A by x -5 and B by x - 3

fraction becomes

   [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  = [tex]\frac{A(x - 5) + B(x - 3)}{(x - 3)(x - 5)}[/tex]

since the denominators of the Left hand side and right hand side are same, we equate the numerators

A(x - 5) + B( x - 3) = x + 7

Using the cover up rule method,

to find A, we substitute x = 3 into the equation so that B becomes zero

A(3 - 5) = 3 + 7

-2A = 10

A = 10/-2

A = -5

To find A put x = 5 so that A = 0

B(5 - 3) = 5 = 7

2B = 12

B = 12/2 = 6

Substituting B and A into the partial fractions above

we have,

 [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

In conclusion the partial fractions are   [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

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The exponential model of the given data is f(t) = 30.18 × 1.06^t.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

Given that,

The average price for office space in 2004 is $30.18.

The average price for office space in 2015 is $66.85.

Suppose the average price in 2004 is taken as y₀.

The given situation can be represented in the form of exponential function f(t) = y₀b^t as,

Take t = 0 for 2004

Then,  f(0) = y₀b^0

⇒ f(0) = y₀ = $30.18.

Then, at 2015, t = 12. Substitute the respective values to get,

f(12) = 30.18 × b^12

⇒ 66.85 = 30.18 × b^12

⇒ b^12 = 66.85 / 30.18

⇒ b = 1.06

Thus in exponential form the given situation can be written as,

f(t) =30.18 × 1.06^t

Hence, the given data can be modeled in exponential function as  f(t) =30.18 × 1.06^t.

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The ratio shows how many times one value is contained in another value.

8 bags of chips = $12

1 bag of chips = $1.5

The unit price of a bag of chips is $1.5

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

There are 4 black and 3 white marbles in a bag.

The ratio of black and white marbles in the bag is 4:3.

We have,

8 bags of chips = $12

Divide both sides by 8.

1 bag of chips = $12/8

1 bag of chips = $3/2

1 bag of chips = $1.5

This means,

1 bag of chips costs $1.5

Thus,

The unit price of a bag of chips is $1.5

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The pitcher that has the lowest number of runs allowed per inning is Randy.

In order to determine the pitcher with the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.

Division is the process of determining the quotient of two or more numbers. It is the process of putting a number into equal groups using another number.

Number of runs per innings = number of runs / number of innings

Number of runs per innings for Randy : 2 / 3 = 0.667

Number of runs per innings for Felix : 4 / 5 = 0.80

Number of runs per innings for Johan: 5 / 7= 0.714

Here is the complete question:

A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.

Which pitcher has the lowest number of runs allowed per inning?

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Answer:

40-20= 20

Step-by-step explanation:

8(5)- 4(5)= 4(5)

40-20=20

The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

sin 18° = √(3 - √5) / 2√2

cos 18° = √ (5 + √5) / 2√2

Now,

Find the value of sin 3° as;

⇒ sin 3° = sin (18 - 15)°

   = sin 18° cos 15° - cos 18° sin 15°

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

   = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

Thus, The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

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Answer:

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace

Step-by-step explanation:

Answer:

$0.45 and a waffle bowl is $1 extra.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.

Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.

It will stand out from the other values in the dataset.

The line plot shows the ages of people visiting a senior center one afternoon.

The data points are,

70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.

If there is an outlier in the set, it would be extremely low or high compared to other points.

But there are no such points.

So there are no outliers.

This means that people visited at the center were all seniors around the same age.

Hence the correct option is (b).

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Probability of drawing a card below a 6 (count an ace as high) is 4/13

Total number of outcome : n(S) = 52

(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}

so , n(E) = 4 × 4 = 16

The probability of drawing a card below a 6 (count an ace as high) = P(E)

[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52

P(E) = 4/13

(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13

Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308

(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6

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The number will x=17 and y=-3 as the sum of two numbers is 14 and the difference between the numbers is 20.

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators. One operand is added to the other in addition. On the provided operands, the operator is accustomed to performing mathematical operations like addition, subtraction, multiplication, division, modulus, etc. Examples of arithmetic operators include: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.

Here,

x+y=14

x-y=20

subtract equation,

2y=-6

y=-3

x+y=14

x-3=14

x=17

The result will be x=17 and y=-3 because the sum of the two numbers is 14 and their difference is 20.

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Answer:

x=28

Step-by-step explanation:

angle b and angle c are the same measure because it is a iso triangle.

you know triangle sum is 180 so 3x+2(x+20)=180. simplify it to 5x=140

divide both sides by 5

x=28

Answer:

x = 28

Step-by-step explanation:

The triangle is isosceles, meaning that the two base angles (x + 20) are congruent. We can then create an equation that states: (x + 20) + (x + 20) + 3x = 180. Simplifying this, we get 5x + 40 = 180. We can then use reverse order of operations to solve it. Subtract 40 from both sides to get 5x = 140. We will then divide both sides by 5 to get x by itself, getting us the equation x = 28.

0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.

The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.

It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.

Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

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The amount of Tritium that bottle contains now will be 439,421.

Consider the function:

y = a (1 - r)ˣ

Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.

Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.

Then the amount of Tritium that bottle contains now will be given as,

y = 856,000 (1 - 0.05)¹³

Simplify the equation, then we have

y = 856,000 (1 - 0.05)¹³

y = 856,000 (0.95)¹³

y = 856,000 (0.51334)

y = 439,421

The amount of Tritium that bottle contains now will be 439,421.

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Answer:

I think the answer is 33?

The simple interest that Oliver needs to pay is $ 90

Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below

Simple interest, I = ptr

where p = principal amount

t = time period in years

r = rate of interest in decimals

Here we have

Oliver borrowed $1,500 to purchase a riding lawn mower  

The rate of interest r = 12%

=> 12/100 = 0.12 (in decimals )

The time period given = 6 months = 0.5 years   [ 6/12 = 0.5 ]  

From the above formula,

The simple interest, I = ptr

=> I = $1,500(0.12) (0.5) = $ 90

Therefore,

The simple interest that Oliver needs to pay is $ 90  

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The volume of the flower box is 7560 cubic inches

The given parameters in the question are:

Length = 5 ft

Upper and lower bases = 18 inches and 10 inches

Height  = 9 inches

The volume of the box can be calculated using the following volume equation

Volume = 0.5 * Height * Length * (Sum of the bases)

Substitute the known values in the above equation So, we have the following equation

Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)

Convert feet to inches

Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)

Evaluate

Volume = 7560 cubic inches

Hence, the volume is 7560 cubic inches

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The theorem that proves that the triangles are congruent is the Hypotenuse-leg (HL) Congruence Theorem. The correct option is the first option - HL Congruence Theorem

From the question, we are to determine by what theorem of postulate the triangles can be proven congruent.

From the Hypotenuse-leg theorem which states that "if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent".

From the given diagram, we can observe that the hypotenuse of the first triangle is congruent to the hypotenuse of the second triangle. Likewise, we can observe that one of the legs of the first triangle is congruent to the one of the legs of the other triangle.

Hence, the triangles are congruent by the Hypotenuse-leg theorem.

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In  linear equation, No of marker is 5 and no of pencil is 3 .

What is a linear equation example?

Myles has 12 markers and 20 pencils.

take LCM of 12 and 20  = 60

no of 12 markers = 5

no of 20 pencils = 3

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84.78 mm² is area of circle .

What is a circle ?

radius of the circle = 27 mm

area of the circle = πr²

                          =  3.14 * 27

                         =  84.78 mm²

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THE percent error is, 5

hence,THE percent error is, 5

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Answer: 13

Step-by-step explanation:

20(.65) = 13

Hope that helps!

1/2 is the probability of getting at least one answer correct

Given that: the exam has 4 multiple choice with 5 possible answers. This means there are 20 possible choices ( 5×4 = 20).

That means each problem has a probability of 1/20 correct answer. The probability of getting at least one answer means you either get one, two, three or four correct answers. Thus:

P (at least one correct) = P(1) + P(2) + P(3) + P(4)

                                      = 1/20 + 2/20 + 3/20 + 4/20

                                      = (1+2+3+4)/20

                                     = 10/20

                                     =   1/2

Therefore, the probability of getting at least one answer correct is 1/2

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The probability of getting at least one answer correct is equal to 7

That I guess at least one answer correctly means that I could get all four answers correct or three answers correct or two answers correct or only one answer correct. The probability of getting any one answer is 1/4 and probability of not getting an answer is 1 - 1/4=3/4. Or implies addition.

probability of getting all four answers correct = 1/4 +1/4 + 1/4 + 1/4 = 4/4 = 1

probability of getting three answers correct = 1/4 +1/4 + 1/4 + 3/4 = 6/4 = 3/2

probability of getting two answers correct = 1/4 +1/4 + 3/4 + 3/4 = 8/4 = 2

probability of getting all four answers correct = 1/4 +3/4 + 3/4 + 3/4 = 10/4 = 5/2

The probability of getting at least one answer correct = 1 + 3/2 + 2 + 5/2

The probability of getting at least one answer correct = (2 + 3 + 4 + 5)/2

The probability of getting at least one answer correct = 14/2

Thefore, the probability of getting at least one answer correctly is the whole number 7

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