A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unac- ceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.016 mm. (a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm? Calculate a P-value to draw conclusions. State any necessary assumptions about the underlying distribution of the data. (b) Construct a 95% lower confidence bound for o. (c) Use the confidence bound in part (b) to test the hypothesis.

By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

DE is the midsegment of AB and AC.

AD≅BD and AE≅EC.

The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

DE=1/2BC

5=1/2(10)

5=5

Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

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Vanessa can buy a maximum of x oranges, where x is the number of oranges she can buy at the store. We can represent this mathematically as an inequality by letting x represent the number of oranges she can buy and setting it equal to the total amount of money she has minus the cost of the eggs divided by the cost of each orange:

x ≤ ($20 - $3) / $0.50

This inequality tells us that Vanessa can buy at most x oranges as long as the total cost of the oranges (x * $0.50) is less than or equal to the amount of money she has remaining after buying the eggs ($20 - $3).

In other words, Vanessa can buy at most x oranges as long as the total cost of the oranges is less than or equal to $17.50. This means she can buy at most 35 oranges, since 35 * $0.50 = $17.50. Therefore, the inequality that represents the maximum number of oranges Vanessa can buy is:

x ≤ 35.

   The probability that the sample mean will be within ±5 of the population mean is 0.6826

If the population is normally distributed, the sample means will be normally distributed even with smaller samples. [This is known as the Central Limit Theorem, which states that when a large number of random samples are drawn from a population, the means of these samples will be normally distributed.]

Z=X-μ/σ

Given here, σ = 50 , μ =200 , σₓ = 5 , n = 100 ,                                                                      

                     z = 205-200/5    z = 195-200/5

we get z= ±1

From the z table, we get P( z= -1)  = 0.1587

From the z table we get P( z= 1)  = 0.8413

Thus the final answer is = 0.8413- 0.1587

                                        =  0.6826

Hence,  the probability that the sample mean will be within ±5 of the population mean is  0.6826

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The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:

9 = -3m + b

8 = -2m + b

Subtracting the second equation from the first equation gives us:

1 = -m

So the slope of the function is -1. Substituting this value back into either equation gives us:

9 = -3(-1) + b

9 = 3 + b

6 = b

So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.

The other two representations can be solved in the same way to find the equations of those functions.

The required next term at the end of the sequence is 43.

Arithmetic progression is the series of numbers that have common differences between adjacent values are equal.

here,
1, 2, 4, 7, 12, 19, 30,
As
the sequence is the prime addition of the number, as.
1,
1 + 1 = 2
2 + 2 = 4,

4 + 3 = 7
7 +  5 = 12
12 + 7 = 19
19 + 11 = 30
30 + 13 = 43

Thus, At the end of the sequence, the required next term is 43.

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The value of the x is 3.26556.

What is the Intersecting Chord Theorem?

When two chords intersect each other inside a circle, the products of their segments are equal.

We have,

It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.

One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).

According to Intersecting Chord Theorem:

This theorem states that A×B is always equal to C×D no matter where the chords are.

A.B = C.D

(x+10) * (x+1) = (x) * (5x+1).

x² + x + 10x + 10 = 5x² + x

x² + x + 10x + 10 - 5x² - x = 0

-4x² + 10x + 10  = 0

using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get

x=−0.765564

x = 3.26556

Hence, the value of the x is 3.26556.

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Ma'am there is nothing to solve...

:<

Answer:

Step-by-step explanation:

Yes there is literally nothing to solve:(

Answer:

y < 13x – 15

Step-by-step explanation:

13x – y < 15

–y < –13x +15

divide both sides by (–)

–(–y) < –(–13)x –(15)

y < 13x – 15

The two events a and b are independent if and only if (a) Events a and b are independent  .

What are Independent Events ?

Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .

The probability of two independent events can be mathematically represented as  P(A and B) = P(A) × P(B) .

So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent  .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Two events, a and b are independent if and only if

Which of the following statements is true of a and b?

(a) Events a and b are independent

(b) Events a and b are not independent, but they are mutually exclusive

(c) Events a and b are not independent since and .

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The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.

Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.

And we have to prove the statement.

According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.

Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.

Here the collection {Ux} is a covering of A by sets open in X.

And the finite collection of them {U1, ..,Un} covers A because A is compact.

Here the open set U = U1 U....U Un contains A and it is disjoint from

V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.

Therefore, here there exists disjoint open sets U and V containing A and B, respectively.

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Answer:

The area of the square is larger than the area of the rectangular field.

Answer:

Slope of the line, [tex]m_{1} = -\frac{1}{2}[/tex]

Slope of parallel line, same as the slope above

Slope of perpendicular line, [tex]m_{2} = 2[/tex]

Step-by-step explanation:

Parallel line: [tex]m_{1} = m_{2}[/tex]

Perpendicular line: [tex]m_{1} * m_{2} = -1[/tex]

[tex]y = mx +b[/tex]

Where, m = slope

Thus, in the equation provided, the slope is [tex]-\frac{1}{2}[/tex]

Finding the slope of perpendicular line:

[tex]m_{1} * m_{2} = -1\\m_{2} = \frac{-1}{m_{1}}\\m_{2} = -1 * -2\\m_{2} = 2[/tex]

After reducing the product in the lowest form and changing to mixed fraction , the answer is  [tex]3\frac{3}{4}[/tex]  .

In the question ,

it is given that ,

the two numbers are 2/8 and 15 ,

we have to find the product without using the calculator and express it in lowest form and then convert the improper fraction in to mixed fraction .

So , the product of 2/8 × 15  = 30/8

in lowest form it is 15/4 .

after converting the improper fraction 15/4  in mixed form ,

we get ,

15/4 = [tex]3\frac{3}{4}[/tex].

Therefore , the product of 2/8 × 15 is [tex]3\frac{3}{4}[/tex]  .

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Superman pro

Step-by-step explanation:

Superman pro

The data are statistically significant at level = 0.05, but not at level = 0.01.

Given-

H0: μ = 115

HA: μ ≠ 115

The sample mean = 120

The standard deviation = 25

Standard error of mean 2.5

Solution-

If  z = (xbar- μ ) / SE

Then the solution would be

z = (120-115) / 2.5

z = 2

P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.

Therefore the answer is technically at .05 level of significance.

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the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.

To find the 25th percentile:

25th percentile: 25% of 32 = 8th number = 13

Count the total number of values in the data set, which is 32

Calculate 25% of 32, which is 8

Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13

To find the 50th percentile:

50th percentile: 50% of 32 = 16th number = 21

Count the total number of values in the data set, which is 32

Calculate 50% of 32, which is 16

Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21

To find the 75th percentile:

75th percentile: 75% of 32 = 24th number = 29

Count the total number of values in the data set, which is 32

Calculate 75% of 32, which is 24

Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29

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Therefore ,the water level is rising  by 0.1388 ft/min when h is 1.2 feet deep and  the water is being pumped at rate of 0.8625 cubic feet per min when water is rising at 3/8 inch/min

A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The concept of length and volume are related.

Here,

Given: A trough has a 12 foot length and a 3 foot top width. Three-foot-high isosceles triangles make up its ends. 12f 3 ft 31

So the first case:

using this we find the rate of Volume,

So,

=> dV/dt = length * height *dh/dt

=> dV/dt = 12 * 1.2 *dh/dt

=> 2 = 12*1.2* dh/dt

=> 2 = 14.4 * dh/dt

=>dh/dt = 2/14.4

=>dh/dt = 0.1388 ft/min

Therefore ,the water level is rising  by 0.1388 ft/min when h is 1.2 feet deep .

Second case:

Since water level is rising by 3/8 inch per min =0.03125 feet/min

=> dV/dt = length * height *dh/dt

=> dV/dt = 12 * 2.3 *0.03125

=>dV/dt = 0.8625 cubic feet per min

Therefore , the water is being pumped at rate of 0.8625 cubic feet per min.

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Answer:

Step-by-step explanation:

its 2

Answer: 8/3

Step-by-step explanation:

In this equation, x=-2

so

f(-2)=-1/6 (1/4)^(-2)

(1/4)^(-2)=4^2=16

f(-2)=-1/6 16

I am going to assume that it's (1/6)*(1/4)^x meaning:

f(-2)=16/6

=8/3

I hope I assumed correctly.

Answer:

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

Given function:

Find f(-2), by plugging in the value of x:

Answer:

You did not provide the choices, but the first step to find the result of the operation using standard algorithm is to set up a long division

The value of the amount will be $721.40.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

500 dollar deposit for 20 years with a interest rate of 2%.

Now,

We know that;

The formula for amount is,

⇒ [tex]A = P (1 + r)^n^t[/tex]

Where, A is total amount, P is principle amount, r is interest rate.

Here, We have;

P = $500

t = 20 years

r = 2%

Substitute all the values, we get;

⇒  [tex]A = P (1 + r)^n^t[/tex]

⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]

⇒ A = 500 × 1.02²⁰

⇒ A = 500 × 1.44

⇒ A = $721.40

Thus, The value of the amount = $721.40

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By using p-value hypothesis test,we find that the mean delivery time actually exceeds 34 minutes.

It is a number calculated from a statistical test that describes how you are found a particular set of observation ,if the null hypothesis were true.P-values are used in hypothesis testing to help to decide whether to reject the null hypothesis .The lower the p-value the greater the statistical significance of observation differences.

The null hypothesis states that as the assumption that there is no change , no difference and no relationship between two variables.The alternate hypothesis stated that there is a change, difference and relationship between two variables or group.

let we use p-value test

Let u=average time spend on deliveries

so,null hypothesis H0;u[tex]\leq[/tex]34 minutes

    alternate hypothesis HA; u >34

Now the decision rule based on the p-value to whether null hypothesis should be accepted or rejected is given by;

.If hypothesis p-value of test statistical is less than the level of significance,then we will our null hypothesis.

.If the p-value of test statistical is more than the level of significance.then we will not reject our null hypothesis.

Here, we assume that the level of significance is 5%.

Since the p-value test statistics is less than the level of significance as 0.029<0.05.

so,we have evidence to reject our null hypothesis.

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Answer: 3 11/15  please mark brainliest If I helped you.

the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is

12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that

is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct

(a) Determinant: det(A) = -18; Rank: rank(A) = 4. The determinant and rank are non-zero, so the vectors are linearly independent.(b) Determinant: det(A) = 0; Rank: rank(A) = 3. The determinant is zero and the rank is less than 4, so the vectors are linearly dependent.

(a)

2 4 5 -3

-3 2 7 0

9 2 4 6

3 2 -6 5

Det = -18

(b)

1 -1 3 2

-1 2 4 -5

3 -4 2 9

7 2 1 3

Det = 0

The determinant and rank of the vectors can be used to determine whether or not they are linearly dependent. If the determinant is non-zero and the rank is equal to the number of vectors, then the vectors are linearly independent. If the determinant is zero and the rank is less than the number of vectors, then the vectors are linearly dependent.

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The function  y = x⁴ + 7 is decreasing on (-∞ , 0) and increasing on (0 , ∞) .

In the question ,

it is given that ,

the function is y = x⁴ + 7 ,

we have to show that function y  is decreasing on (-∞ , 0) and increasing on (0 , ∞) .

differentiating the function y = x⁴ + 7 , with respect to x ,

we get ,

y'(x) = d/dx(x⁴ + 7) = 4x³

putting y'(x) = 0 , then 4x³ = 0 ;

x³ = 0 that means , x = 0 .

thus , the critical number is ⇒ x = 0 .

y'(-1) = 4(-1)³ = -4   So , it is decreasing

y'(1) = 4(1)³ = 4    So , it is increasing .

Therefore , the function y is decreasing in (-∞ , 0) and increasing in (0 , ∞) .

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Answer:

DF is congruent to FG

Step-by-step explanation:

segment subractive property means to subract a part of a segment from another if they are equal. If we do this in this situation, we will see that DF is congruent to FG

       Statement                                        Reason                          

Proof:

Let's start of by solving for the length of AC, which is just the sum of lengths AB and BC, which is 10 + 3 = 13 units.

Because of our second given, AC ≅ EG, we know that EG is also 13 units in length. Also, from our first given, BC ≅ EF, we know that EF is 3 units.

We also know that the length of EG is the sum of lengths EF and FG so we can write the equation

EG = EF + FG

13 = 3 + FG

FG = 10 meaning FG is 10 units

a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%

b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user is 23%

Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.

The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.

The question state that

Pr(D) = 0.10

Pr(D') = 0.90

Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)

Pr(P/D') = 0.05

a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')

⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)

⇒ Pr(D/P) = 0.098/(0.098+0.045)

⇒ Pr(D/P) = 0.098/0.143

⇒ Pr(D/P) ≈ 0.6853

⇒ Pr(D/P) ≈ 69%

b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')

⇒ Pr (P*2/D') = 0.05*0.05

⇒ Pr (P*2/D') = 0.0025

⇒ Pr (P*2/D') = 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)

⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)

⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604

⇒ Pr (D'/P*2) = 0.00225/0.09829

⇒ Pr (D'/P*2) ≈ 0.2289

⇒ Pr (D'/P*2) ≈ 23%

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All the possible values for the number 'x' will be less than or equal to 1,350.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The remainder of a number and 5 in addition to 25 is something like 45.

Let the number be 'x'. Then the inequality is given as,

x / (5 + 25) ≤ 45

x / 30 ≤ 45

x ≤ 1,350

All the possible values for the number 'x' will be less than or equal to 1,350.

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