Suppose that 13% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) a. What is the (approximate) probability that X is at most 30? b. What is the (approximate) probability that X is less than 30? c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?

Answer:

x=2√2 is the answer

Step-by-step explanation:

x²=8

TAKING SQUARE ROOT ON BOTH SIDES

√x²=√8

x=√2×2×2

x=√2²×√2

x=2√2

i hope this will help you

Answer:

The value of x is -2.828 or 2.828

Step-by-step explanation:

In order to eliminate of square of x, you have to square root both sides :

[tex] {x}^{2} = 8[/tex]

[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]

[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]

[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]

Answer:

1/2

Step-by-step explanation:

There is a 50/50 chance for the coin to land either heads or tails. Convert that to probability and it is 1/2.

The only time a coin would not be 50/50 chance is if the coin is weighted.

Answer:

1/2 is probability

becoz one side is head or one is tail

Answer:

  4.25

Step-by-step explanation:

The growth factor is 1 more than the growth rate. The growth rate is the rate of increase in a given time period.

  1 +325% = 1 +3.25 = 4.25

The growth factor is 4.25.

_____

The "increase" amount is what is added to the original. The growth factor is the multiplier of the original.

  x + 325%·x = x(1 +3.25) = 4.25x

Answer:

Step-by-step explanation:

Hello!

Given the independent variable X and the dependent variable Y (see data in attachment)

The regression equation is

^Y= b₀ + bX

Where

b₀= estimation of the y-intercept

b= estimation of the slope

The formulas to manually calculate both estimations are:

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

[tex]b_0= \frac{}{y} - b*\frac{}{x}[/tex]

n=7

∑X= 42

∑X²= 292

∑Y= 49

∑Y²= 403

∑XY= 249

[tex]\frac{}{y} = \frac{sumY}{n} = \frac{49}{7} = 7[/tex]

[tex]\frac{}{x} = \frac{sumX}{n} = \frac{42}{7} = 6[/tex]

[tex]b= \frac{249-\frac{42*49}{7} }{292-\frac{42^2}{7} }= -1.13[/tex]

[tex]b_0= 7- (-1.13)*6= 13.75[/tex]

^Y= 13.75 - 1.13X

Using the raw data you can calculate the coefficient of determination as:

[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}[/tex]

[tex]R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84[/tex]

This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X

I hope this helps!

Answer:

x=-4

Step-by-step explanation:

[tex]2x^2+8x=x^2-16[/tex]

Move everything to one side:

[tex]x^2+8x+16=0[/tex]

Factor:

[tex](x+4)^2=0[/tex]

By the zero product rule, x=-4. Hope this helps!

Answer:

x=-4

Step-by-step explanation:

Move everything to one side and combine like-terms

x²+8x+16

Factor

(x+4)²

x=-4

Answer: 150

Step-by-step explanation:

How many months are in a year? 12.

The average rate per month is therefore 1800/12 = 150.

Hope that helped,

-sirswagger21

Answer:

x2 = 60

Step-by-step explanation:

If the variables x and y are inversely proportional, the product x * y is a constant.

So using x1 and y1 we can find the value of this constant:

[tex]x1 * y1 = k[/tex]

[tex]12 * 15 = k[/tex]

[tex]k = 180[/tex]

Now, we can use the same constant to find x2:

[tex]x2 * y2 = k[/tex]

[tex]x2 * 3 = 180[/tex]

[tex]x2 = 180 / 3 = 60[/tex]

So the value of x2 is 60.

Answer:

[tex]\boxed{\sf \ \ \ m = -\dfrac{tn}{t-s} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let s assume that m+n is different from 0

we have this equation and we need to find m as a function of t, s, and n

[tex]t=\dfrac{ms}{m+n}[/tex]

<=>

[tex](m+n)*t=ms\\\\<=> tm+tn=sm\\<=> (t-s)m = -tn\\<=> m = -\dfrac{tn}{t-s}[/tex]

for t-s different from 0, so t different from s

hope this helps

Answer:

1 : 500,000

Step-by-step explanation:

The scale of a map scale refers to the relationship (or ratio) between the distance on a map and the corresponding distance on the ground.

In the given map:

1 mm​(map) = 500 m ​(actual)

1 meter = 1000 millimeter

Therefore:

500 meters = 1000 X 500 =500,000 millimeter

Therefore, the scale ratio of the map is:

1:500,000

Answer:

Step-by-step explanation:

Number of frames =3 frames

If each frames contain 2 photos, the total number of photos in all the 3 frames will be 3*2 = 6photos

Since we have 6 photos in total, the fraction that shows one photo will be ratio of one out of the six photos and this is represented as 1/6

Answer:

The diagram of the question is missing, I found a matching diagram, and it is attached to this answer

The 3D object produced is a cone with height 8 and diameter 8 (radius 4)

Step-by-step explanation:

A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.

when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.

Answer:

There. You didn't ask for and explanation!

Step-by-step explanation:

The solution of expression is,

⇒ 343

We have to given that;

The expression is,

⇒ [tex]49^{\frac{3}{2} }[/tex]

Now, We can simplify with rational exponents as,

⇒ [tex]49^{\frac{3}{2} }[/tex]

⇒ [tex](7^2 )^{\frac{3}{2} }[/tex]

Apply rule of exponent as,

⇒ [tex]7^2^* ^{\frac{3}{2} }[/tex]

⇒ 7³

⇒ 7 × 7 × 7

⇒ 343

Thus, The solution of expression is,

⇒ 343

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ6

Answer:

7x+ 4y +8

Step-by-step explanation:

12x -5x +4y +15-7

= 7x + 4y + 8

Answer:

Step-by-step explanation:

15 + 12x - 5x +4y - 7

= 15 - 7 + 12x - 5x + 4y

= 8 + 7x + 4y

= 7x + 4y + 8 ( rearranging the terms )

Hope this helps

Plz mark it as brainliest!!!!

Answer:

Step-by-step explanation:

Let the number be x.

The reciprocal of the number will be 1/x

If the sum of the number and its reciprocal is 41/20, this can be represented as;

[tex]x+\frac{1}{x} = 41/20\\\frac{x^{2}+1}{x} = \frac{41}{20} \\20x^{2} +20 = 41x\\20x^{2} -41x+20 = 0\\[/tex]

Uisng the general formula to get x

x = -b±√b²+4ac/2a

x = 41±√41²-4(20)(20)/2(20)

x = 41±√1681-1600/40

x = 41±√81/40

x = 41±9/40

x = 50/40 or 32/40

x = 5/4 or 4/5

if the value is 5/4, the other value will be 4/5

The numbers are 5/4 and 4/5

The smaller value is 4/5

The larger value is 5/4

Answer:

a=5/4 or 4/5

Therefore, the smaller value = 4/5

The larger value = 5/4

Step-by-step explanation:

Let the number be represented by a

And it's reciprocal be represented by 1/a

So we have

a + 1/a = 41/20

Cross Multiply

20( a +1/a) = 41

20a +20/a =41

Find the LCM which is a

20a² + 20 = 41a

20a² + 20 - 41a =0

20a² - 41a +20 = 0

20a²-25a - 16a + 20 =0

5a(4a - 5) -4( 4a - 5) = 0

(5a - 4)(4a - 5) = 0

5a - 4 = 0

5a = 4

a = 4/5

or

4a - 5 = 0

4a =5

a = 5/4

Therefore, the number which is represented by a is

1) a = 4/5 while it's reciprocal which is 1/a is 5/4

or

2) a = 5/4 which it's reciprocal which is 1/a = 4/5

Therefore, the smaller value = 4/5

The larger value = 5/4

Answer:

34285714285/100000000000

Step-by-step explanation:

To write 0.34285714285 as a fraction you have to write 0.34285714285 as the numerator and put 1 as the denominator. Now you multiply the numerator and denominator by a number that makes the numerator to a whole number.

And finally, we have:

0.34285714285 as a fraction equals 34285714285/100000000000

Answer:

m∠x ≈ 32°

Step-by-step explanation:

We can see that we have to use tan∅ to solve this (opposite over adjacent)

tan(x) = 7/11

x = tan^-1 (7/11)

x = 32.4712

Answer:

A.32

Step-by-step explanation:

tan(x) = 7/11

x = tan^-1 (7/11)

x = 32.4712

Answer:

Domain is x and Range is y

Step-by-step explanation:

Domain-(16,-15,22,-1,-6)

Range-(5,-17,-16,-4,-14)

Answer:

a) Percentage of standardized test takers that scored 550 or less = 76.4%

b) Percentage of standardized test takers that scored 524 = 0.782%

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 514

Standard deviation = σ = 50

a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)

We first normalize or standardize 550

The standardized score for any is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (550 - 514)/50 = 0.72

To determine the required probability

P(x ≤ 550) = P(z ≤ 0.72)

We'll use data from the normal distribution table for these probabilities

P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%

The normal curve for this question and the b part are sketched in the first attached image to this solution.

b) Percentage of standardized test takers that scored 524 = P(x = 524)

On standardizing,

z = (x - μ)/σ = (524 - 514)/50 = 0.20

For this part, since it's an exact probability, we will use the normal distribution formula

P(z = Z) = [1/(σ√2π)] × e^(-z²/2)

Since z = (x - μ)/σ

It can be written properly as presented in the second attached image to this question.

Putting x = 524 or z = 0.20 in this expression, we get

P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%

Hope this Helps!!!

Answer:

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Step-by-step explanation:

A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],

Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?

So

[tex]x_{1} = x_{2} = \sqrt{3}[/tex]

[tex]x_{3} = -2[/tex]

Then

[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]

Since [tex]\sqrt{3} = 1.73[/tex]

[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Answer:

[tex]\frac{x}{5} - 4[/tex]

Step-by-step explanation:

You are dividing x by 5 and then subtracting 4.

Answer:

x/5 - 4

Step-by-step explanation:

The quotient of a number x and 5 refers to division of both terms.

x/5

Four less than the quotient refers to subtraction.

x/5 - 4

Answer:

196x^2y

Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

The Pythagorean theorem is

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the sides that form the right angle), and c is the length of the hypotenuse (the side opposite the right angle.)

Answer: Attached

Step-by-step explanation:

Answer:

a) 23.73% probability that all five of them have a landline

b) 76.27% probability that at least one of them does not have a landline

c) 99.90% probability that at least one of them does have a landline

Step-by-step explanation:

For each household, there are only two possible outcomes. Either it has landline service, or it does not. The probability of a household having landline service is independent of other households. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

25% of households in a certain country had no landline service.

This means that 100-25 = 75% have, so [tex]p = 0.75[/tex]

Pick five households form this country at random.

This means that [tex]n = 5[/tex]

a) what is the probability that all five of them have a landline?

This is P(X = 5).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.75)^{5}.(0.25)^{0} = 0.2373[/tex]

23.73% probability that all five of them have a landline

b) what is the probability that at least one of them does not have a landline?

Either all have, or at least one does not have. The sum of the probabilities of these events is 100%.

From a), 23.73% probability that all five of them have a landline

100 - 23.73 = 76.27

76.27% probability that at least one of them does not have a landline

c) what is the probability that at least one of them does have a landline?

Either none have a landline, or at least one has. The sum of the probabilities of these events is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.75)^{0}.(0.25)^{5} = 0.0010[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0010 = 0.9990[/tex]

99.90% probability that at least one of them does have a landline

Answer:

To find it's percentage divide $5.60 by

$17.50 and multiply it by 100%

That is

5.60/ 17.50 × 100%

= 32%

Hope this helps you

Answer:

(x-1) ( x -i) (x+i)

Step-by-step explanation:

x^3 -2x^2 +x-2

Factor by grouping

x^3 -2x^2      +x-2

x^2(x-2)      +1(x-2)

Factor out (x-2)

(x-2) (x^2+1)

Rewriting

(x-1) ( x^2 - (-1)^2)

(x-1) ( x -i) (x+i)

Answer:

Should be b

Step-by-step explanation:

Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.

You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.

Then, since you know the imaginary roots have to be conjugates, you get B.

Answer:

3.784

Step-by-step explanation:

Answer:

13 students

Step-by-step explanation:

At least 30 and fewer than 67 makes it 30-66

So,

30-66 => 13 students

Answer:

16

Step-by-step explanation:

There are two columns in the diagram.

The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23

So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:

20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66

Answer:

Degrees of freedom for independence  in chi-square statistic

ν = ( r-1) (s-1) =6

Step-by-step explanation:

Explanation:-

Given data  chi-square test for independence is being used to evaluate the relationship between two variables

Given "A" is classified into 3 categories

Second 'B' is classified into 4 categories

In this chi-square test, we test if two attributes A and B under consideration are independent or not

We will assume that

Null Hypothesis : H₀: The two variables are independent

Degrees of freedom in chi-square test for independence

ν = ( r-1) (s-1)

Given data 'r' = 3  and  's' = 4

Degrees of freedom for independence

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Test statistic

                       χ ²  =  ∑  [tex]\frac{(O-E)^{2} }{E}[/tex]

This question is based on Chi-square test. Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].

Given:

Chi-square test for independence is being used to evaluate the relationship between two variables . Given "A" is classified into 3 categories . Second 'B' is classified into 4 categories

According to the question,

In this chi-square test, we would be test if two attributes A and B under consideration are independent or not.

Let assumed that,  null Hypothesis : H₀: The two variables are independent

Now, degrees of freedom in chi-square test for independence is,

 ⇒ ν = ( r-1) (s-1)

It is given that, 'r' = 3  and  's' = 4.

Thus, degrees of freedom for independence is,

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Therefore, test statistic be,

[tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex]

Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].

For more details, prefer this link:

https://brainly.com/question/23879950

Question Completion

PIE CHART NUMBERS:

Answer:

0.000063

Step-by-step explanation:

Number of Respondents, n=1400

Probability that they would rate their financial shape as​ excellent = 0.09

Number of Those who would rate their financial shape as excellent

=0.09 X 1400

=126

Therefore:

The probability that 4 people chosen at random would rate their financial shape as​ excellent

[tex]=\dfrac{^{126}C_4 \times ^{1400-126}C_0}{^{1400}C_4} \\=\dfrac{^{126}C_4 \times ^{1274}C_0}{^{1400}C_4}\\=0.000063 $(correct to 6 decimal places)[/tex]

Answer:

Read below

Step-by-step explanation:

To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.

I hope this helps!