The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eight syringes taken from the batch. Suppose the batch contains 5% defective syringes. A button hyperlink to the SALT program that reads: Use SALT.
(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, , 7 and 8 defective syringes in a random sample of eight syringes.
(b) Find μ. (Enter your answer to two decimal places.) μ = syringes What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.) syringes
(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.) (
d) Find Ï. (Round your answer to three decimal places.) Ï = syringes

Answer:

B

Step-by-step explanation:

The equivalent expression is (x + 2√3i) (x - 2√3i).

What is a Polynomial Equation?

The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.

Given polynomial is,

x² + 12

We need to find it's equivalent expression for that see the options

Solve the option (a)

(x + 2√3i) (x - 2√3i)

Now, solve this if we get equal to x² + 12 that means that option is answer

x(x - 2√3i) + 2√3i(x - 2√3i)

x² - 2xi√3 + 2xi√3 -  2√3i *  2√3i

x²  -  12 i²

we know, i² = -1

so, we get

x² + 12

We get the answer by 1st option. If you solve other options you'll get different answer.

Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).

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To determine how much data is enough to estimate the average weight of this population with a 95% confidence and an error not superior to 15 grams, we would need to use a statistical sample size calculator or consult a statistical table. Factors that would need to be considered include the desired confidence level, the desired margin of error, and the standard deviation of the population.

Using a sample size calculator, we can input these values and determine the required sample size. For example, with a 95% confidence level, a margin of error of 15 grams, and a standard deviation of 87 grams, the required sample size would be approximately 38 children. This means that we would need to measure the weight of at least 38 male children who are 10 weeks old in order to estimate the average weight of the population with a 95% confidence and an error not superior to 15 grams.

It is important to note that this is just an estimate and the actual sample size may vary depending on the specific characteristics of the population being studied. Additionally, it is always a good idea to consult with a statistician or other expert to ensure that the appropriate sample size is used in any statistical analysis.

The equation represents that, Miles could rent the meeting room for t ≤ 16 hours.

What is inequality?

The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.

The total cost for Miles to rent the meeting room for t hours is given by the equation C = 21 + 4t. We are trying to find the number of hours t for which C is equal to or less than $85.

We can solve this problem by setting up the inequality 21 + 4t ≤ 85 and solving for t.

Subtracting 21 from both sides gives us 4t ≤ 64.

Dividing both sides by 4 gives us t ≤ 16.

Thus, Miles can rent the meeting room for t hours, where t is less than or equal to 16. This means that he can rent the room for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 hours.

Hence, the equation represents that, Miles could rent the meeting room for t ≤ 16 hours.

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The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

What is a polynomial function?

Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.

By using the given table, we can plot the points on the graph and we can draw a graph

• Fitted coefficients:

a = 9

b = -9

c = -1

d = 1

Then we can prepare the polynomial as

y = 9 - 9x - x² + x³

Now write down in the standard form, we get

f(x) = x³ - x² -9x + 9

Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

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We would expect 198 of the intervals to contain the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

Given that Mary wishes to estimate the mean height of women aged 18-24.

picks a sample of 100

Women aged between 18 and 24 and constructs a 99% confidence interval for the population mean.

If Mary were to repeat this procedure 200 times in total, she would obtain

200 different confidence intervals.

A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful.  A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable.

I would expect 99%×200 or 198 of the intervals to contain the mean.

Hence, would expect 198 of the intervals to contain the mean.

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Answer:(-6 5/6)

Step-by-step explanation:

-12.5=-12-1/2

-5 2/3= -5-2/3

=(-12 3/6)-(-5 4/6)

=(-6 5/6)

gimme brainlliest

The decision for rejecting the null hypothesis is μ = 8.4

In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.

Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.

Here we have to determine the decision for rejecting the null hypothesis.

While we looking into the the given question we have identified the following values,

Standard deviation = 1.0

Mean pressure = 8.4 pounds/square

Level of significance = 0.05

Sample size = 24

According to these values the null and alternative hypothesis is written as,

H0 = μ = 8.4

Hx = μ ≠ 8.4

Therefore, H0 = μ = 8.4 is the decision for this one.

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The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Given,
To determine the value of the unknowns in the matrix,

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,

2z -18 = 12
z = 15

10 - 6 = 4y
y = 1

Thus,  the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

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Answer:

[tex]85 \sqrt{5} [/tex]

The percentage of the council members who voted in favor of the tax is 50%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the council has 76 members out of which 38 members voted in favor of the tax.

The percentage amount of members who favor the tax is:
(38/76) × 100%

= 50%

Hence, the percentage of the council members who voted in favor of the tax is 50%.

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The change represents growth and rate of increase is 4.2%

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Given that, an exponential function y = 970(1.042)ˣ

When the growth rate is greater than 1, then the function represents a growth.

The general form equation is:

y(x)= a(1+r)ˣ such that r is the growth percent.

So,

1+r = 1.042

r = 0.042

r = 4.2%

Hence, the growth rate is 4.2%

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Answer:

                  1

log₂√2 = ------

                  2

Step-by-step explanation:

I'm assuming the equation looks like this:

2¹⁽² = √2

                  1

log₂√2 = ------

                  2

I hope this helps!

Step-by-step explanation:

30/4=7.4

30/5=6

6/3=2

Alex went to the moves 4 times that year.

The missing numbers are 3 hours = 180 minutes 24 hours = 1 day

24 months = 2 years

What are numbers ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.

1. 5 × x = 45

   45 / 5 = x

    x = 9

45 ÷ 5 = 9

2. 200 + 600 = 800

300 + 400 = 700

3. 3 hours = 180 minutes

     3 * 60 minutes

24 hours = 1 day

24 months = 2 years

12 * 2 = 24

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Answer: 1/2

Step-by-step explanation:

Use rise over run. Up 1, over 2.

And so on. Find nice points on the graph to practice slope with!

Answer:

C.

Step-by-step explanation:

For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.

For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.

It will take 220.8 hour, Teresa to knit 265 squares

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that the relationship between the number of hours Teresa spends

knitting and the number of squares she completes for a blanket.

We need to find the hours does it take Teresa to knit 265 squares.

Now Based on the equivalent ratios  we have;

Teresa's Knitting /Completed Squares

10/12 = x / 265

Thus, Now cross multiplication we get;

x = 265(10/12)

x = 220.8

The answer is 220.8

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Answer:

always true , because 120+60=180

Share of the each person is 1/12. And the above situation can be represented in the given picture.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.

When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.

To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.

First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.

Here we have

6 people equally share 1/2 a pan of macaroni and cheese  

As we know 1/2 means half

By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts

=> (1/2) ÷ 6 =  [tex]\frac{ \frac{1}{2} }{6}[/tex]  = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]  

Therefore,

Share of the each person is 1/12. And the above situation can be represented in the given picture.

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Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given,

5 machines take 9 days,

5 x 9 = 45 machines day

45/15 = 3 days

Hence "Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines".

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Answer:

x = 222:2 and x = 2

Step-by-step explanation:

(2x-123):3=33

(2x – 123):3 = 33

2x – 123 = 33.3

2x – 123 = 99

2x = 99 + 123

2x = 222

x = 222:2

x = 111

200-8.(2x+7)=112

200 – 8.(2x + 7) = 112

-8.(2x + 7) = 112 – 200

-8.(2x + 7) = -88

2x + 7 = (-88):(-8)

2x + 7 = 11

2x = 11 – 7

2x = 4

x = 4:2

   x = 2

I hope my answer helps you.

Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

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Answer:Pemdas

Step-by-step explanation:Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

Answer:

5 cups

Step-by-step explanation:

6bananas =2cups

6(2cups)+6(2cups)+3(1cup)= 15 bananas

5cups of blueberries

Answer: z=3x+1

Step-by-step explanation:

1. Distribute 6 through the parentheses

18x=6z-6

2. Move the z variable to the left side and x variable to the right

-6z= -6-18x

3. Divide both sides by -6 in order to get z by itself

z=1+3x

4. Reorder the terms using commutative property

z=3x+1

Answer:

John = 14 ; Van = 26

Step-by-step explanation:

V = 12 + J

V - 2 = 2(J-2)

12 + J - 2 = 2J - 4

J + 10 = 2J - 4

2J - J = 10 + 4

J = 14

V = 12 + 14

V = 26

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

Since the length of 15 is divided between the circumference of the circle and the perimeter of the square,

2πr + 4s = 15 ⇒ s = (15 - 2πr ) / 4

A = πr2 + s2 = πr2 + [ (15 - 2πr ) / 4]2 = πr2 + (225 - 60πr + 4π2r2) / 16

A = π(1 + π/4)r2 - (15/4)πr + 225/16

dA/dr = 2π(1 + π/4)r - (15/4)π = 0 ⇒ r = (15/4)π / [2π(1 + π/4)] = 15 / (8 + 2π)

Since A(r) is concave up, it has a minimum at

r = 15 / (8 + 2π)

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

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2/ ( 1 + x) ( 1 - x) is express  into partial fractions.

With an example, what is a partial fraction?

The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].

                        The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.

= 2/(1-(x^2))

= 2 / (1)² - (X)²

=  2/ ( 1 + x) ( 1 - x)

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The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28

From the given information, we are to determine the expression that is equivalent to the given expression

The given expression is

(ab⁷)⁴

To determine the expression that is equivalent to this expression, we will expand the given expression

Expanding the expression

(ab⁷)⁴

Applying the distributive exponent law of indices,

(a)⁴ × (b⁷)⁴

Simplifying

a⁴ × b²⁸

= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸

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Answer:

I think it's a4b28

Step-by-step explanation: