The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.02 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)
(a) Calculate P(10.99 ? X ? 11.01) when n = 16.
(b) How likely is it that the sample mean diameter exceeds 11.01 when n = 25?

To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.

Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.

Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:

ad^2 + cd^2 = ac^2

We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:

bd^2 + cd^2 = ac^2

We also know that c lies on ab, so we can write:

ac = ab - bc

Substituting this into our equation, we get:

bd^2 + cd^2 = ab^2 - 2abbc + bc^2

Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:

bd^2 + y^2 = (x + y)^2 - 2xy + x^2

Simplifying, we get:

bd^2 - x^2 = 2xy - y^2

Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.

To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.

Since angle adb = angle bad, we can write:

2 angle adb + angle acd = 180 degrees

Substituting in the values of our angles, we get:

2 angle adb + 90 degrees = 180 degrees

Solving for angle adb, we get:

angle adb = 45 degrees

Now, we can use the fact that triangle adb is isosceles to write:

angle bad = (180 - 45)/2 = 67.5 degrees

Finally, we can use the law of sines to relate bd and x:

bd/sin(67.5) = x/sin(45)

Simplifying, we get:

bd = x

Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.

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In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.

In right triangle ABC,

BC is the base.

Midpoint of AB is D.

CD bisects ACB.

Measure of ∠ACD = Measure of ∠BCD

AC = 4

BC = 7.5

AD = 3

BD = x

CD bisects angle ACB and intersect at midpoint of AB at point D.

This implies

BD / AD = BC / AC

⇒x / 3 = 7.5 / 4

⇒ x = ( 7.5 × 3 ) / 4

⇒ x = 22.5 / 4

⇒ x = 5.625

Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.

The above question is incomplete , the complete question is :

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

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Answer:

C. 2

Step-by-step explanation:

A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.

In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².

The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.

The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.

So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.

Answer: Let's call the total number of action figures you need to complete your collection "x". Based on the information given, we know that 30 action figures is 40% of x, so we can write the equation:

30 = 0.40x

To solve for x, we'll divide both sides of the equation by 0.40:

x = 30 / 0.40

x = 75

So, the total number of action figures you need to complete your collection is 75. Since you purchase 5 action figures per week, it will take you 75 / 5 = 15 weeks to complete your collection.

Step-by-step explanation:

The amount of money the company makes per shirt  $18.90

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes

                                 = X/n

To calculate the expected profit per shirt, we need to consider the two possible outcomes:

the shirt is defective or not defective.

If the shirt is not defective, the company makes a profit of $20.

If the shirt is defective, the company incurs a cost of $35 and no profit.

The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:

= 1 - 0.02

= 0.98.

Therefore, the expected profit per shirt can be calculated as:

Expected profit = (probability of not defective) x (profit per non-defective shirt)

+ (probability of defective) x (cost per defective shirt)

Expected profit = 0.98 x $20 + 0.02 x (-$35)

Expected profit = $19.60 - $0.70

Expected profit = $18.90

So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.

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Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.

Step-by-step explanation:

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The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively. dont forget mark me brainliest

Answer:

No

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 32 + 4x + 20 + 4x + 20 = 180

9x + 72 = 180  ( subtract 72 from both sides )

9x = 108 ( divide both sides by 9 )

x = 12

then the 3 angles are

x + 32 = 12 + 32 = 44°

4x + 20 = 4(12) + 20 = 48 + 20 = 68°

4x + 20 = 68°

an obtuse angle is greater than 90°

none of the 3 angles in the triangle are obtuse

Answer:

No

Step-by-step explanation:

All angles of a triangle add up to 180°.

4x + 20 + 4x + 20 + x + 32 = 180

1. Simplify

9x + 72 = 180

2. Subtract 72 from both sides.

9x = 108

3. Divide both sides by 9.

x = 12

Replace x by 12 in each angle.

-  12 + 32 = 44°

-  4(12) + 20 = 68°

-  4(12) + 20 = 68°

All of the angles are less than 90°, so they aren't obtuse.

Answer: -3, 0

Step-by-step explanation:

If a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, an endpoint of this rotated segment is (-3, 0) and (-7, 0).

In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of this line segment with endpoints (0,−3) and (0,−7), the coordinate of its image;

(x, y)                            →            (y, -x)

Point (0,−3)          →     Point (-3, 0)

Point (0, -7)          →     Point (-7, 0)

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Answer:

$10576.38

Step-by-step explanation:

To calculate the investment amount required to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money you have after "t" years,

P is the initial investment amount (what you want to find),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the investment will be compounded for.

In this case,

r = 0.036

n = 12 (because the interest is compounded monthly)

t = 15

So, we can plug in the values into the formula and solve for P:

A = P * (1 + 0.036/12)^(12 * 15)

$23711 = P * (1.003)^(180)

$23711 = P * 2.2375

Dividing both sides by 2.2375:

P = $23711 / 2.2375

P = $10576.38

So, to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you would need to invest $10576.38. Rounded to the nearest dollar, this amount is $10576.

Answer:

Marianna will have $19,700 in her annuity after 6 years.

Step-by-step explanation:

To find the amount of money in the annuity after 6 years, we need to calculate the compound interest earned over that time period.

First, let's find the interest rate per quarter: 8% annual interest divided by 4 quarters per year = 2% interest per quarter.

Next, we'll calculate the number of quarters that the money is invested: 6 years x 4 quarters per year = 24 quarters.

Now we can use the formula for compound interest to find the total amount of money in the annuity after 6 years:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = initial investment ($10,000 in this case)

r = interest rate per quarter (2% or 0.02)

n = number of times the interest is compounded in a year (4)

t = number of years invested (6)

Plugging in the values:

A = $10,000 * (1 + 0.02)^(24)

A = $10,000 * 1.96634438

A = $19,663.44

Rounding to the nearest hundred dollars: $19,700

So, Marianna will have $19,700 in her annuity after 6 years.

The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.

What is meant by combination?

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.

Given,

Number of engineers in the faculty = 20

Number of engineers required to form a committee = 20

1) Number of ways when either engr. Marzo or engr. William is only present.

   Excluding Marzo and William, we have 18 engineers.

So we can select 6 engineers from these 18 = 18C6 =  [tex]\frac{18!}{6!12!}[/tex] = 18564

Number of ways we can select only one from Marzo and William = 2C1 = 2

So the total number of combinations for forming a committee = 18564 + 2 = 18566

2) Engr. Cara and Eng. Danny are present.

   Engr. Hillary is not considered.

So we have to select 5 members from the rest of the 15 people

Number of combinations are = 15C5 = 3003

3) Engineers Gilliam, Fernando and Ophelia are selected.

    Now we have to select the rest of the 4 members from the remaining 15 people

Number of combinations = 15C4 = 1365

Therefore the number of combinations of different engineers are found to form a 7 member committee.

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Answer:B

Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4

Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .

To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:

Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.

Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.

Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².

Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.

Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.

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Complete question is:

A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .

Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95

Answer:

(-3,-1)

Step-by-step explanation:

The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.

Answer:

The correct answer is D. inventory; number of employees on payroll. An accountant records on hand to note a company's inventory, which is the stock of goods available for sale or use in the production process. The number of employees on payroll refers to the human resources aspect of a company, which is separate from the inventory.

All of the options which are true of similar shapes include the following:

A. They must be the same shape.

D. They can be different sizes.

In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.

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Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.

Step-by-step explanation:

To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:

r(2) = cov(X(t), X(t-2)) / var(X(t))

where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).

To calculate the covariance, we'll use the following formula:

cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)

where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:

var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)

First, let's calculate the mean of X(t):

mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51

Next, let's calculate the covariance between X(t) and X(t-2):

cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3

Finally, let's calculate the variance of X(t):

var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7

Plugging in these values, we can find the autocorrelation at lag 2:

r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018

So the autocorrelation of the time series X at lag 2 is approximately -0.018.

Answer:

Step-by-step explanation:

Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:

rate = cost/length = 92 cents/23 inches = 4 cents/inch

Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:

cost = rate * length = 4 cents/inch * 34 inches = 136 cents

So, 34 inches of wire will cost 136 cents.

Step-by-step explanation:

the trick is to find the "norm" rate, which is the rate for one unit.

from there we can get the rate for any number of units just by multiplying.

so,

23 in for 92 cents.

that means the rate is

23/92 = 23/(23×4) = 1/4

so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.

so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)

1/4 × 34/34 = 34/136

that means 34 inches cost 136 cents (= $1.36).

since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.

[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]

Answer: Vertical asymptotes are = [tex]-4, 1,4[/tex]

Horizontal asymptote = [tex]y=0[/tex]

Step-by-step explanation:

If you need explanation just say you want...

The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.

The union of the two sets depict all the terms present in both the sets.

Thus, the value of (A ∪ B) is:

(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}

The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:

(A ∩ B) = {7}

Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

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The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = ( -4x² + 36 ) / ( x + 3 )

On simplifying , we get

g ( x ) = -4 ( x² - 9 ) / ( x + 3 )

On further simplification , we get

g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )

g ( x ) = -4 ( x - 3 )

g ( x ) = -4x + 12

Now , the function has a vertical asymptote at ( 0 , 12 )

The function has a horizontal asymptote at ( 3 , 0 )

Hence , the function is solved

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Answer:

at least one x-intercept

at least one y-intercept

domain of x

Step-by-step explanation:

took ed2023

Answer:  -151

Step-by-step explanation:  

First Plug everything in

-7(5)^(2)+2(5)+2(7)

Then use order of operations and first deal with the exponent

-7(25)+2(5)+2(7)

then multiply left to right

-175+10+14

combine

so the answer is -151

Answer:

x^2 + 3x + 2

Step-by-step explanation:

(x + 2) * (x + 1) =

= x * x + x * 1 + 2 * x + 2 * 1 =

= x^2 + x + 2x + 2 =

= x^2 + 3x + 2

Using division operation, the number of containers that Linden would get from his supply of milk is 79 containers.

Division operation involves the dividend divided by the divisor to obtain a result called the quotient.

Division operation is one of the four basic mathematical operations, including multiplication, addition, and subtraction.

Total liters of milk = 237

The content of the liter containers = 3 liters

The number of containers = 79 (237 ÷ 3)

Thus, based on division operation, Linden, who is sharing 237 liters of milk in containers will need 79 3-liter containers.

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The answers include the following:

This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.

3x = 18

x = 18/3 = 6

x+9 =22

x = 22-9 = 13

x/4 = 6

x = 6 × 4 = 24

x-12 =19

x = 19+12 =31

2x + 9 = 25

2x = 25-9 =16

x=16/2 = 8

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The slope for:

1 = 1/2  (Option E)

2 = 2 (Option C)

3 = -1/2 (Option H)

4 = -2 (Option A)

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The formula for slope (m) is given as:

m = Rise/Run = y2-y1/x2-x1

(x1,y1) = Coordinates of the first point in the line

(x2,y2) = Coordinates of the second point in the line.

1) The points are:

x1= -2

y1 = 2

x2 =2

y2  = 4

m = (4 - 2) / (2 - (-2))

m = 2 / 4

m = 1/2

Thus, Δy/Δx = 1/2

2) The points are:

x1= -1

y1 = -12

x2 =5

yx  = 0

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

m = (0 - (-12)) / (5 - (-1))

m = 12 / 6

m = 2

Thus, Δy/Δx = 2


3) Where the points are:
x1= 2

y1 = -6

x2 = - 4

y2  = -3

Substituting the given values, we get:

m = (-3 - (-6)) / (-4 - 2)

m = 3 / (-6)

m = -1/2

Thus, Δy/Δx = -1/2


4)  Where the points are:
x1= 0

y1 = 3

x2 = 1.5

y2  = 0

Substituting the given values, we get:

m = (0 - 3) / (1.5 - 0)

m = -3 / 1.5

m = -2


Thus, Δy/Δx = -2

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The annual interest rate on the saving account is 5%.

Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.

To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.

Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:

$200 = $1,000 * r * 4

r = $200 / ($1,000 * 4)

r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.

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