A manufacturing machine has a 10% defect rate. If 8 items are chosen at random, what is the probability that at least one will have a defect?

Answer:

12 units^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 ( 6 ) * 4

A = 1/2 (24)

    = 12 units^2

Answer: 0.655

Step-by-step explanation:

Let X be a random variable that represents percent of fat calories that a person in America consumes each day.

As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).

Sample size : n= 16

The probability that the average percent of fat calories consumed is more than 35:

\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)

Hence, Required probability =0.655

Answer:

46 boxes

Step-by-step explanation:

1012 / 22 = 46

When the 2 graphs are the same. It'll be infinitely many solutions.

System Equations are to find the intercepts of graphs so just think that when 2 graphs are same, that means they both intercept each others infinitely.

So the answer is clearly C.

Answer:

English bru?

Step-by-step explanation:

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Answer:

1/9 = 0.1111111

Step-by-step explanation:

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

The points on this graph which satisfies the given requirements are (4, 2).

A graph can be defined as a type of chart that's commonly used to graphically represent data (points) on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A domain can be defined as the set of all real numbers for which a particular function is defined. For this graph, the vertex of the parabola is (4, 2).

A range can be defined as the set of all real numbers that connects with the elements of a domain. For this graph, we can observe that only real numbers which lies between -4 and 2 are connected to the values on the x-axis of the domain.

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Answer:

$4884 to the nearest $.

Step-by-step explanation:

By proportion it is  2275 *  (23*28) / (15*20)

= $4884

Answer:

Check pdf

Step-by-step explanation:

Answer:

The ratio given cannot be used to find the answer

Answer:

471 cm^2

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.14" was replaced by "(314/100)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    t*t-((314/100))=0

Step by step solution :

STEP

1

:

           157

Simplify   ———

           50

Equation at the end of step

1

:

       157

 t2 -  ———  = 0

       50

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  50  as the denominator :

          t2     t2 • 50

    t2 =  ——  =  ———————

          1        50  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

t2 • 50 - (157)     50t2 - 157

———————————————  =  ——————————

      50                50    

Trying to factor as a Difference of Squares:

2.3      Factoring:  50t2 - 157

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  50  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

 50t2 - 157

 ——————————  = 0

     50    

STEP

3

:

When a fraction equals zero :

3.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 50t2-157

 ———————— • 50 = 0 • 50

    50  

Now, on the left hand side, the  50  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  50t2-157  = 0

Solving a Single Variable Equation:

3.2      Solve  :    50t2-157 = 0

Add  157  to both sides of the equation :

                     50t2 = 157

Divide both sides of the equation by 50:

                    t2 = 157/50 = 3.140

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     t  =  ± √ 157/50  

Answer:

"Option A" is the right alternative.

Step-by-step explanation:

Other provided preferences weren’t comparable to the same circumstances in question.

Answer:King John wanted to wage a war with France to win back his ancestors land, and taxed the barons and people heavily.

Step-by-step explanation:

Answer:

la respuesta es la primera ( a )

Step-by-step explanation:

Answer:

2800

Step-by-step explanation:

Sounds complicated, but it's just multiplication, it would just be 400 x 7

Answer:

x= 9.37

y = 17.69

Step-by-step explanation:

in order to find the answer, use the trigonometries.

First finding x which is tan(32) = x/15

x = tan(32)15

and Y is cos(32) = 15/y

y = 15/cos(32)

I hope this helps

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

The required distance between the foot of the ladder to the wall is 14.14 feet.

Using trigonometry, we can find that the distance from the wall (x) is given by:
x = 20sin(45°)
  = 20(√2/2)
  = 10√2 feet.

This is approximately equal to 14.14 feet when rounded to two decimal places.

The correct answer is C. 14.14 feet.

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The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Answer:

The answer is 0.267949192

Step-by-step explanation:

I hope that is enough numbers.

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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Answer:

True

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

x = 23 and y = 45

Step-by-step explanation:

x + y = 68

y = x + 22

substitute into your equation for x + y = 68

x + (x+22) = 68

combine like terms

2x + 22 = 68

2x = 46

x = 23

Now, use this to solve for y = x + 22

y = 23 + 22

y = 45

Answer:

8.33% probability that she does, in fact, have the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Has the disease

Probability of a positive test:

10% of 100-1 = 99%

90% of 1%

So

\(P(A) = 0.1*0.99 + 0.9*0.01 = 0.108\)

Positive test and having the disease:

90% of 1%

\(P(A \cap B) = 0.9*0.01 = 0.009\)

What is the conditional probability that she does, in fact, have the disease

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.108} = 0.0833\)

8.33% probability that she does, in fact, have the disease

The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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