A quality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. The proportion of bottles that actually have such a flaw is only 0.0002. If a bottle has a flaw, the probability is 0.995 that it will fail the inspection. If a bottle does not have a flaw, the probability is 0.99 that it will pass the inspection.

or, 144° + x° = 180°

or, x° = 180° - 144°

or, x° = 36°

or, x = 36.

x = 36

Hope it helps.

Do comment if you have any query.

The four integers in increasing order are 4, 6, 14, 15.

Let the integers, in increasing order, be

a, b , c , d

We know the the  sum of the  smallest two must  be  the least sum...so...

a + b   = 10    (1)

And we know that the sum   of the  largest two must be the  greatest sum....so

c + d  =  29      (2)

And it must be that  

b + d  =   21      (3)

Subtracting  (3)  from (2)    we have that

c - b  =  8     so

b + 8  = c

So,

a + b + c + d  = 39

a + b + (b + 8) + d = 39

a + 2b + d  = 31

a + d  =   31  - 2b .... (4)

But  

a + d  = 19  

If  a + d   = 19 , then by (4)  ;b  = 6 ; c = 14 ; d  = 15  and  a  = 4.

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Answer:

(x + 7)2 + (y + 1)2 = r2.

To get we use point (8, 7): (8 + 7)2 + (7 + 1)2 = r2, r2 = 225 + 64 = 289 = 172.

So, equation of circle: (x + 7)2 + (y + 1)2 = 289

Step-by-step explanation:

The fourth-order accurate finite difference approximation is:

u00(x) = c−2u(x − 2h) + c−1u(x − h) + c0u(x) + c1u(x + h) + c2u(x + 2h) + O(h4).

Compute the coefficients using the matlab code fdstencil.m and check that they satisfy the system you determined in part (a).

Test this finite difference formula to approximate u

00(1) for u(x) = sin(2x) with values of h from the array hvals = log space(-1, -4, 13). Make a table of the error vs. h for several values of h and compare against the predicted error from the leading term of the expression printed by  fdstencils.

You should observe the predicted accuracy for larger values of h. For smaller values, numerical cancellation in computing the linear combination of u values impacts the accuracy observed.

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The probability that the student will fail, given that he guesses the answers, is 0.227.

Since there are only two possible outcomes for each question (true or false),

the probability of guessing a correct answer is 1/2 = 0.5.

Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.

To find the probability of failing the exam,

we need to find the probability of answering less than 11 questions correctly.

Using the binomial probability formula,

the probability of getting k successes (correct answers) in n trials (questions) is given by:

P(k) = (n C k) * p^k * q^(n-k)

where p is the probability of success (getting a correct answer),

q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.

In this case,

n = 17, p = 0.5, and

q = 0.5.

The number of ways to get less than 11 correct answers is:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)

Substituting the values:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015

P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146

P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586

P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558

P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268

P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327

P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732

P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537

P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573

P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013

P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015

Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857

Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857

The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).

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Answer:

d=2

Step-by-step explanation:

10+3d=16

3d=6

divide both sides by 3

d=2

Subtract 10 from both sides.

Subtract 10 from 16 to get 6.

Divide both sides by 3.

Divide 6 by 3 to get 2.

.Answer:

A)

y = 60°

B)

x = 11

∡YXW = 82°

∡WXZ = 8°

Step-by-step explanation:

A)

y, x are complementory angles

then:

x + y = 90

.y = 2x

then:

x + 2x= 90°

3x = 90°

x = 90/3

x = 30

y = 2x

y = 2*30

y = 60°

B)

Angle YXW an angle WXZ are complementory angles:

then:

(7x+5) + (3x-25) = 90°

7x + 3x + 5 - 25 = 90

10x -20 = 90

10x = 90 + 20

10x = 110

x = 110/10

x = 11

then:

7x+5 = 7*11 + 5 = 77 + 5 = 82°

3x - 25 = 3*11 - 25 = 33 - 25 = 8°

Answer:

A)

y = 60°

B)

x = 11

∡YXW = 82°

∡WXZ = 8°

Four two-digit numbers are constructed from numbers 1, 2, 3, ..., 8. The largest number of  primes that could possibly formed among those four numbers is 3 numbers.

A prime number is a whole number greater than 1 which only divisible by 1 and itself. Example of prime numbers are 2, 3, 5, 7, ...

We want to form 4 two-digit numbers from, 1, 2, 3, 4, 5, 6, 7, 8.

Recall that: other than 2, all even numbers are not prime since they are divisible by 2. Hence, from those numbers, we look at which odd two-digit numbers are prime.

We have four odd numbers in the list that can construct two-digit odd numbers: 1, 3, 5, 7.

However, two-digit numbers with 5 as its second digit is not prime since they are exactly divisible by 5.

Therefore, now we only have 3 numbers (1, 3, 7) that can construct two-digit odd numbers. Hence, the largest number of primes that could possibly formed is 3 numbers.

Example, the constructed four two-digit numbers are:

47, 53, 61, 28

47, 53, and 61 are prime, while 28 is not.

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Answer:

Step-by-step explanation:

(x+4)(x+5) = 0

x = -4

x = -5

Answer:

Step-by-step explanation: To find out what grade Sally needs to earn on her fifth and last math test to achieve a 90 average, we  use the following steps:

Step 1: Add the total points Sally has received: 80 + 82 + 92 + 98 = 352.

Sally has taken 4 tests so far.

Step 2: Find the total marks required for a 90 average on 5 tests: 90 x 5 = 450.

Step 3: Find the score Sally needs to achieve on her fifth test by subtracting the points earned  from the total required points: 450 - 352 = 98.

Therefore, Sally needs to earn a grade of 98 on her 5th and last test to achieve a 90 average on all five tests this semester.

the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.

Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.

Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.

The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.

Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.

The dimensions of the parking lot are 100 yards by 400 yards.

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The given statement "The misuse of statistics is sometimes intentional." is True, because there are instances where people intentionally misuse statistics to manipulate or deceive others.

The misuse of statistics can be an intentional act by individuals or organizations to manipulate or deceive others. This is often done by selectively choosing data or statistics that support a particular argument or position, while ignoring or downplaying information that does not support it.

One way this can be achieved is by distorting graphs or charts. For example, a bar chart can be designed to visually exaggerate the differences between data points, making the differences appear more significant than they actually are. This can be done by adjusting the scale of the chart or by changing the width of the bars.

Another way that statistics can be misused is by making false claims based on the data. For example, someone may use a correlation between two variables to imply a causal relationship, even though there may not be any evidence to support this claim.

Similarly, statistics can be used to mislead people by presenting them in a way that is misleading. For example, a statistic may be presented without any context or compared to an irrelevant baseline, making it appear more significant or less significant than it actually is.

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Answer:

If the cost price (CP) is 380 and the gain percentage is 25%, we can use the following formula to find the selling price (SP):

SP = CP + (gain percentage/100) * CP

Substituting the given values, we get:

SP = 380 + (25/100) * 380

SP = 380 + 95

SP = 475

Therefore, the selling price is 475.

Step-by-step explanation:

Answer:

Answer → 63°

Step-by-step explanation:

» m<3 and m<4 are supplementary angles.

☑ Supplementary angles are angles that measure up to 180°

\({ \tt{m \angle 3 + m \angle 4 = 180 \degree}} \\ { \tt{117 \degree + m \angle 4 = 180 \degree}} \\ { \tt{m \angle 4 = 180 \degree - 117 \degree}} \\ { \tt{m \angle 4 = 63 \degree}}\)

Answer: 0.032, 18, 4224, 7.58

Step-by-step explanation:

5. 5 L = 5000 mL = 5000 \(cm^{3}\)

5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L

6. There is (13 - 11) x 20 x 10 = 400 \(cm^{3}\) left unoccupied in the box

400/23 = 17.4 so it takes 18 balls to overflow the water

7. 1 mL = 1 \(cm^{3}\)

(a) 22 x 12 x 16 = 4224 \(cm^{3}\) = 4224 mL

(b) 2 L = 2000 mL = 2000 \(cm^{3}\)

22 x 12 = 264

2000/264 = 7.58 cm

As x approaches 0, the limit of p(x) does not exist.

To determine the limit of p(x) as x approaches 0, we can evaluate the behavior of the function from both sides of x = 0.

If we approach from the left side (negative values of x), the expression cos²2(x)/sin(2x) approaches positive infinity as sin(2x) approaches 0 and cos²(x) remains positive.

However, if we approach from the right side (positive values of x), the expression cos²(x)/sin(2x) approaches negative infinity as sin(2x) approaches 0 and cos²(x) remains positive.

Since the function has different limits from the left and right sides, the limit of p(x) as x approaches 0 does not exist.

Therefore, the statement "As x approaches 0, the limit of p(x) does not exist" accurately describes the behavior of the function.

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The 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.

If an 80% confidence interval and a 90% confidence interval are constructed from the same sample data, the 80% confidence interval will be narrower than the 90% confidence interval.

To understand why this is the case, we need to know that a confidence interval is a range of values within which we estimate the true population parameter lies. The level of confidence associated with the interval represents the probability that the true parameter falls within that range.

In this scenario, an 80% confidence interval means that there is an 80% probability that the true parameter lies within the interval. On the other hand, a 90% confidence interval means that there is a 90% probability that the true parameter falls within the interval.

To construct a narrower interval, we need to have a higher level of confidence. As the confidence level increases, the range of possible values also widens to accommodate the higher probability. Therefore, the 80% confidence interval will be narrower than the 90% confidence interval.

In conclusion, the 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.

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Answer:

A and E

Step-by-step explanation:

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\) ← distance formula

it is important that the x and y coordinates are placed correctly, that is not mixed together.

First version

let (x₁, y₁ ) = X (- 5,  4 ) and (x₂, y₂ ) = Y (7, 15 ) , then

XY = \(\sqrt{(7-(-5)^2+(15-4)^2}\) → A

or

Second version

let (x₁, y₁ ) = Y (7, 15 ) and (x₂, y₂ ) = X (- 5, 4 ) , then

XY = \(\sqrt{(-5-7)^2+(4-15)^2}\) → E

Answer: I think it is C. I might be wrong but I tried

Step-by-step explanation:

The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

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Answer:

Ella scored 10 points.

Step-by-step explanation:

35 - 15 = 20

20/2 = 10

Answer:

Los radios de los círculos son \(r_{1} \approx 9.995\), \(r_{2} \approx 2.013\), \(r_{3} \approx 7.592\), respectivamente.

Las áreas de los círculos son \(A_{1} \approx 313.845\), \(A_{2} \approx 12.730\), \(A_{3} \approx 181.077\), respectivamente.

Step-by-step explanation:

La circunferencia (\(s\)) se calcula mediante la siguiente fórmula:

\(s = 2\pi\cdot r\) (1)

Donde \(r\) es el radio del círculo.

Una vez hallado el radio, se determina el área de la figura geométrica (\(A\)) mediante la siguiente fórmula:

\(A = \pi\cdot r^{2}\) (2)

Si conocemos que las circunferencias son \(s_{1} = 62.8\), \(s_{2} = 12.65\) y \(s_{3} = 47.7\), respectivamente:

1) Radios de los círculos

\(r_{1} = \frac{s_{1}}{2\pi}\), \(r_{2} = \frac{s_{2}}{2\pi}\), \(r_{3} = \frac{s_{3}}{2\pi}\)

\(r_{1} \approx 9.995\), \(r_{2} \approx 2.013\), \(r_{3} \approx 7.592\)

2) Áreas de los círculos

\(A_{1} = \pi\cdot r_{1}^{2}\), \(A_{2} = \pi\cdot r_{2}^{2}\), \(A_{3} = \pi\cdot r_{3}^{2}\)

\(A_{1} \approx 313.845\), \(A_{2} \approx 12.730\), \(A_{3} \approx 181.077\)

The solution to the given system of linear equations is x = 4, y = 20

From the question, we are to determine solution to the given system of equations

The given system of equations is

x+y=6x=y+4

Thus, we can write that

x + y = 6x ----------- (1)

and

6x = y + 4 ------------(2)

Solve the two equations simultaneously

From equation (1)

x + y = 6x

y = 6x - x

y = 5x --------- (3)

Substitute into equation (2)

6x = y + 4

6x = 5x + 4

6x - 5x = 4

x = 4

Substitute the value of x into equation (3)

y = 5x

y = 5(4)

y = 20

Hence, the solution to the given system of linear equations is x = 4, y = 20

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Answer:

-3x-5 x-4 I this work good luck

Answer:

-(3x-5) (x-4)

Step-by-step explanation:

-3x^2+17x-20

Factor -1 out of -3x^2

-(3x^2)+17x-20

Factor -1 out of 17x

-(3x^2)-(-17x)-20

Rewrite -20 as -1(20)

-(3x^2)-(-17x)-1(20)

Factor -1 out of -(3x^2)-(-17x)

-(3x^2-17x)-1(20)

Factor -1 out of -(3x^2-17x)-1(20)

-(3x^2-17x+20)

Factor.

-((3x-5)(x-4))

Final Anwser:

-(3x-5) (x-4)

In this case, we'll have to carry out several steps to find the solution.

We must analyze the graph to find the solution.

Step 01:

The domain is reflected on the x-axis and the range is reflected on the y-axis

domain: (-oo , oo)

range: (-3 , oo)

Step 02:

relative minimum:

1. (- 2.5 , -1) = ( -5/2 , -1)

2. ( 3 , -3 )

relative maximum

1. ( 0, 5)

That is the full solution.

Answer:

150 each times

Step-by-step explanation:

Just subtract.Ex:300-150=150

Answer: veasy

Step-by-step explanation: it is a rectangle then it's area will be length *breadth =45cm*26=1170cm^2.

Answer:

1170 or 0.117 m^2

Step-by-step explanation:

Answer:

22, and -22

Step-by-step explanation:

22x22=484

-22x(-22)=484

Step-by-step explanation:

18x²-8

= 2(9x²-4)

= 2(3x+2)(3x-2)

18x² - 8

Common factor is 2.

=》18x² - 8

=》2 (9x²- 4) [option C].

_____

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