Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. The folllowing table gives the type of defect and the number of lenses with that defect. Assume categories are mutually exclusive.

Defect Type Frequency
Scratch 5734
Right shaped - small 4654
Flaked 1554
Wrong axis 1594
Chamfer wrong 1829
Crazing, cracks 1387
Wrong shape 1718
Wrong PD 1822
Spots and bubbles 1291
Wrong height 1602
Right shape - big 1538
Lost in lab 975
Spots/bubbles - intern 997


a) Find the probability that a randomly selected defect from the table will be in the categor "Crazing, cracks" or the category "Right shaped - small".
Give your answer as a fraction.


Give your answer rounded to three decimal places.


b) Find the probability that a randomly selected defect is not in the category "Crazing, cracks".

Given your answer as a fraction.


Give your answer rounded to three decimal places.

Answers

Answer 1

The probabilities for this problem are given as follows:

a) Crazing, cracks or Right shaped - small: (4654 + 1387)/26695 = 0.226.

b) Not Crazing cracks: (26695 - 1387)/26695 = 0.948.

How to calculate a probability?

The parameters that are needed to calculate a probability are listed as follows:

Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

5734 + 4654 + 1554 + 1594 + 1829 + 1387 + 1718 + 1822  + 1291 + 1602 + 1538 + 975 + 997 = 26695.

The probability for item a is given as follows:

(4654 + 1387)/26695 = 0.226.

The probability for item b is given as follows:

(26695 - 1387)/26695 = 0.948.

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Related Questions

Solve for x
65°
40°
X+85°

Answers

Answer:

x is equal to -10 degrees.

Step-by-step explanation:

To solve for x in the given angles, we need to find the value that makes the sum of the angles equal to 180 degrees.

Given angles:

1. 65°

2. 40°

3. x + 85°

To find x, we can set up the equation:

65° + 40° + (x + 85°) = 180°

Combine like terms:

(65 + 40 + 85)° + x = 180°

Simplify:

190° + x = 180°

To isolate x, we subtract 190° from both sides:

x = 180° - 190°

Simplify:

x = -10°

Therefore, x is equal to -10 degrees.

A Sandwich shop has three types of sandwiches ham turkey and chicken. Each sandwich can be ordered on white bread or multi grain bread. Customers can add any combination of the four available toppings. See if this scenario involves a premutation, combination or the multiplication counting principle then find the number of possibilities

Answers

Answer:

the answer is 24

Step-by-step explanation:

Multiply

Number of sandwich options: 3

Number of bread options: 2

Number of topping options:

3 sandwich options 2 bread options 4 topping options

= 24

Solve the system of linear equations using elimination.

−5x + 3y = −19
−x − 3y = −11

Answers

By solving the system of linear equations using elimination x= 5 and y=2.

-5x + 3y = -19  is  equation 1

-x - 3y = -11  is equation 2

Add Equation 1 to Equation 2

-5x + 3y + -x - 3y = -19+ -11

(3y-3y=0 as a result y term can be eliminated)

gives -6x =  -30

Dividing,

  = x = 5

Put it in equation 1,  we get

-5*5 + 3y = -19

=-25 + 3y = -19

= 3y  = 25-19 = 6

= y = 2

Solving the equations we get x = 5  and y = 2.

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what expession is eqvalant to 7/12 times 2

Answers

[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \frac{7}{6} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

Please help me as soon as possible .

Answers

The length of the minor arc CE in the given circle, with an angle CDE of 62 degrees and a radius CD of 8 units, is approximately 13.645 units, rounded to the nearest hundredth.

To find the length of arc CE (minor arc) in a circle with center D, where m∠CDE = 62 degrees and CD = 8 units (radius), we can use the formula for the length of an arc. The formula is L = rθ, where L represents the arc length, r represents the radius of the circle, and θ represents the central angle subtended by the arc.

In this case, the given angle m∠CDE = 62 degrees and the radius CD = 8 units.

First, we need to convert the angle from degrees to radians since the formula requires the angle in radians. To convert from degrees to radians, we use the conversion factor π/180. So, θ = 62 * (π/180) radians.

Next, we substitute the values into the formula for the length of an arc:

L = rθ

L = 8 * (62 * (π/180))

L ≈ 13.645 units (rounded to the nearest hundredth)

Therefore, the length of arc CE (minor arc) in the given circle, rounded to the nearest hundredth, is approximately 13.645 units.

It's important to note that the length of an arc is directly proportional to the central angle it subtends and the radius of the circle. In this case, the given angle of 62 degrees and the radius of 8 units determine the length of the arc CE.

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Select the correct answer.
Which statement best defines an angle?
A. two rays that share a common endpoint called the vertex
B.
two lines that share a common line segment called the vertex
C.
two line segments that intersect at a point called the vertex
D.
two lines that intersect at a point called the vertex

Answers

Option(A) is the correct answer : A. Two rays that share a common endpoint called the vertex.

An angle is a fundamental concept in geometry that helps us understand the relationship and measurement of lines and shapes. It is formed by two rays that share a common endpoint called the vertex. To fully grasp the concept of an angle, it's important to understand its components and properties.

The rays that form an angle are called the sides of the angle. They extend indefinitely from the vertex in opposite directions, defining the space between them. The endpoint where the rays meet is known as the vertex of the angle.

Angles can vary in size and measurement. The measure of an angle is typically expressed in degrees (°) or radians (rad). A full circle is divided into 360 degrees or 2π radians. Angles smaller than 90 degrees are considered acute angles, while angles exactly 90 degrees are right angles. Angles greater than 90 degrees but less than 180 degrees are called obtuse angles, and angles measuring exactly 180 degrees are straight angles.

Angles have various properties and relationships. When two angles share a common vertex and a common side, they are called adjacent angles. The sum of adjacent angles around a point is always 360 degrees. Angles that have the same measure are called congruent angles.

Understanding angles is crucial in geometry and various other fields, including trigonometry, physics, and engineering. They help us analyze and describe the orientation, position, and spatial relationships of objects in both two-dimensional and three-dimensional spaces.

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Answer:

A. Two rays that share a common endpoint called the vertex.

Step-by-step explanation:

Let s(t) = 4t³42t2 + 120t be the equation of motion for a particle. Find a function for the
velocity.
v(t) = 121² +1-72
Where does the velocity equal zero? [Hint: factor out the GCF.]
t
and t= -2
Find a function for the acceleration of the particle.
a(t) =
Question Help: Video

Answers

The function for velocity is v(t) = 12t² + 84t + 120, the velocity equals zero at t = -2 and t = -5, and the function for acceleration is a(t) = 24t + 84.

To find the function for velocity, we need to take the derivative of the equation of motion, s(t), with respect to time, t. The derivative of s(t) gives us the rate of change of position, which is velocity.

Given: s(t) = 4t³ + 42t² + 120t

To find v(t), we differentiate s(t) with respect to t:

v(t) = 12t² + 84t + 120

So, the function for velocity is v(t) = 12t² + 84t + 120.

To find where the velocity equals zero, we set v(t) = 0 and solve for t:

12t² + 84t + 120 = 0

To solve this quadratic equation, we can factor out the greatest common factor (GCF), which is 12:

12(t² + 7t + 10) = 0

Now, we can factor the quadratic expression inside the parentheses:

12(t + 2)(t + 5) = 0

Setting each factor equal to zero, we get:

t + 2 = 0   -->   t = -2

t + 5 = 0   -->   t = -5

So, the velocity equals zero at t = -2 and t = -5.

To find the function for acceleration, we need to take the derivative of the velocity function, v(t), with respect to time, t. The derivative of v(t) gives us the rate of change of velocity, which is acceleration.

Given: v(t) = 12t² + 84t + 120

To find a(t), we differentiate v(t) with respect to t:

a(t) = 24t + 84

So, the function for acceleration is a(t) = 24t + 84.

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What is the correct expanded form and value of (Four-fifths) cubed?
Four-fifths + four-fifths + four-fifths = StartFraction 12 Over 5 EndFraction
Four-fifths times four-fifths times four-fifths = StartFraction 64 Over 125 EndFraction
StartFraction 4 + 4 + 4 Over 5 EndFraction = StartFraction 12 Over 5 EndFraction
Five-fourths times five-fourths times five-fourths = StartFraction 125 Over 64 EndFraction
Mark this and return

Answers

Answer:

The correct expanded form and value of (Four-fifths) cubed is:

(Four-fifths) cubed = (4/5)³

Expanded form: (4/5) × (4/5) × (4/5)

Value: (4/5) × (4/5) × (4/5) = 64/125

Therefore, the correct expanded form of (Four-fifths) cubed is (4/5) × (4/5) × (4/5), and its value is 64/125.

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Answers

Answer:

[tex]\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2[/tex]

[tex]\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2[/tex]

[tex]\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}[/tex]

Step-by-step explanation:

Question 1

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

[tex]x^2-14x+\left(\dfrac{-14}{2}\right)^2[/tex]

[tex]x^2-14x+\left(-7\right)^2[/tex]

[tex]x^2-14x+49[/tex]

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

[tex]\boxed{a^2 -2ab + b^2 = (a -b)^2}[/tex]

Therefore:

[tex]a^2=x^2 \implies a=1[/tex]

[tex]b^2=49=7^2\implies b = 7[/tex]

Therefore, the perfect square trinomial rewritten as a binomial squared is:

[tex]x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2[/tex]

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

[tex]9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2[/tex]

[tex]9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2[/tex]

[tex]9x^2 + 30x +9 \cdot \dfrac{25}{9}[/tex]

[tex]9x^2 + 30x +25[/tex]

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

[tex]\boxed{a^2 +2ab + b^2 = (a +b)^2}[/tex]

Therefore:

[tex]a^2=9x^2 = (3x)^2 \implies a = 3x[/tex]

[tex]b^2=25 = 5^2 \implies b = 5[/tex]

Therefore, the perfect square trinomial rewritten as a binomial squared is:

[tex]9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2[/tex]

[tex]\hrulefill[/tex]

Question 2

(a) Factor out the leading coefficient 3 from the given expression:

[tex]3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)[/tex]

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

[tex]\boxed{a^2 -2ab + b^2 = (a -b)^2}[/tex]

Factor the perfect square trinomial inside the parentheses:

                        [tex]=3\left(x-\boxed{4}\right)^2[/tex]

(a) Factor out the leading coefficient 1/2 from the given expression:

[tex]\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)[/tex]

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

[tex]\boxed{a^2+2ab + b^2 = (a +b)^2}[/tex]

Factor the perfect square trinomial inside the parentheses:

                        [tex]=\dfrac{1}{2}\left(x+\boxed{8}\right)^2[/tex]

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

A car is traveling at a speed of 40 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in hours? In your computations, assume that mile is equal to kilometers. Do not round your answers.

Answers

The car's speed is approximately 64.37 kilometers per hour, and it will travel 64.37 times the number of hours it is on the road in kilometers.

When converting miles per hour to kilometers per hour, we need to consider that 1 mile is approximately equal to 1.60934 kilometers. Therefore, to find the car's speed in kilometers per hour, we can multiply its speed in miles per hour by the conversion factor of 1.60934.

In this case, the car's speed of 40 miles per hour can be converted as follows:

40 miles/hour * 1.60934 kilometers/mile = 64.3736 kilometers/hour.

Thus, the car's speed is approximately 64.37 kilometers per hour.

To calculate the distance the car will travel in hours, we can use the formula distance = speed × time. Given that the car will be traveling for a certain number of hours, let's say 't' hours, the distance traveled in kilometers can be determined as:

Distance = 64.37 kilometers/hour × t hours = 64.37t kilometers.

Therefore, the car will travel 64.37 times the number of hours it travels in kilometers.

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Aaron contributed $3,100 to his RRSP at the end of every half- year. What was the value of his RRSP after 12.5 years if the RRSP grew at 2.6% compounded semiannually? (Round your final answer to 2 decimal places​

Answers

The value of Aaron's RRSP after 12.5 years, compounded semiannually at a rate of 2.6%, would be approximately $4,197.40.

To calculate the value of Aaron's RRSP after 12.5 years, we can use the formula for compound interest:

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

Where:

A = Final amount (value of RRSP after 12.5 years)

P = Initial contribution per period ($3,100)

r = Interest rate per period (2.6% or 0.026)

n = Number of compounding periods per year (2 since it's compounded semiannually)

t = Number of years (12.5)

Plugging in the values, we have:

A = 3100(1 + 0.026/2)^(2 * 12.5)

Simplifying the expression inside the parentheses:

A = 3100(1 + 0.013)^25

Calculating the value inside the parentheses:

A = 3100(1.013)^25

Using a calculator or a spreadsheet, we can evaluate the expression inside the parentheses to get:

A ≈ 3100(1.354)

A ≈ 4197.40

Therefore, the value of Aaron's RRSP after 12.5 years, compounded semiannually at a rate of 2.6%, would be approximately $4,197.40.

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Use the Venn diagram to complete the contingency table. Then find the probabilities

Answers

A) Using the Venn Diagram to complete the contingency table is as follows:

Contingency Table:

                       Boys     Not boys     Total

Juniors              75            65            140

Not juniors     335          225           560

Total               410          290           700

B) Finding the probabilities is as follows:

1. The probability that a student selected at random is a boy is 41/70.

2. The probability of selecting a boy that is a junior is 15/82.

3. The probability of randomly choosing a student who is a Junior and a boy is 3/28.

4. The probability of randomly choosing a student who is a girl given that she is not junior is 45/58.

5. The probability of randomly selecting a girl is 29/70.

What are the probabilities?

Probability refers to the chance or likelihood of an expected outcome occurring from many possible outcomes, events, or results.

Probability values lie between zero and 1, depending on their levels of certainty, and can be represented as fractions, decimals, or percentages.

A) Contingency Table from the Venn Diagram

                       Boys     Not boys     Total

Juniors              75            65            140

Not juniors     335          225           560

Total               410          290           700

1) The probability that a student chosen at random is a boy = Total number of boys/Total number of students

= 410/700

= 41/70

2) The probability that a boy selected at random is a junior = total number of male juniors / total number of boys

= 75/410

= 15/82

3) The probability of choosing a student that is a junior and a boy = total number of male juniors / total number of students

= 75/700

= 3/28

4. The probability of randomly choosing a student that is a girl given that she is not a junior = total number of girls that are not juniors / total number of girls

= 225/290

= 45/58

5. The probability of randomly selecting a girl = total number of girls / total number of students

= 290/700

= 29/70

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Question Completion:

1. What is the probability that a student selected at random is a boy?

2. What is the probability that a boy selected at random is a Junior?

3. What is the probability of randomly choosing a student who is a Junior and a boy?

4. What is the probability of randomly choosing a student who is a girl given that she is not junior? PC G.)

5. What is the probability of randomly selecting a girl?

A national college researcher reported that 65% of students who graduated from high school in 2012 enrolled in college. Twenty-eight high school graduates are sampled. Round the answers to four decimal places.

a) What is the probability that exactly 16 of them enroll in college?
(b) What is the probability that more than 14 enroll in college?
(c) What is the probability that fewer than 10 enroll in college?
(d) Would it be unusual if more than 23 of them enroll in college?

Answers

(a) Probability of exactly 16 enrolling in college is approximately 0.1487 or 14.87%.

(b) Probability of more than 14 enrolling in college is approximately 0.8622 or 86.22%.

(c) Probability of fewer than 10 enrolling in college is approximately 0.0003 or 0.03%.

(d) It would be considered unusual if more than 23 enrolled in college as the probability is approximately 0.0072 or 0.72%.

(a) To calculate the probability that exactly 16 of the 28 high school graduates enroll in college, we can use the binomial distribution formula.

P(X = 16) = (28 C 16) * (0.65)^16 * (1 - 0.65)^(28 - 16)

Using a binomial probability calculator or formula, we find that P(X = 16) ≈ 0.1487.

The probability that exactly 16 of the sampled high school graduates enroll in college is approximately 0.1487 or 14.87%.

(b) To calculate the probability that more than 14 of the 28 high school graduates enroll in college, we need to find the sum of probabilities for all values greater than 14.

P(X > 14) = 1 - P(X ≤ 14)

Using a binomial probability calculator or formula, we find that P(X > 14) ≈ 0.8622.

The probability that more than 14 of the sampled high school graduates enroll in college is approximately 0.8622 or 86.22%.

(c) To calculate the probability that fewer than 10 of the 28 high school graduates enroll in college, we need to find the sum of probabilities for all values less than 10.

P(X < 10) = P(X ≤ 9)

Using a binomial probability calculator or formula, we find that P(X < 10) ≈ 0.0003.

The probability that fewer than 10 of the sampled high school graduates enroll in college is approximately 0.0003 or 0.03%.

(d) To determine if it would be unusual for more than 23 of the 28 high school graduates to enroll in college, we can compare it to a certain threshold or criterion. A common threshold used is having a probability less than 5%.

P(X > 23) = 1 - P(X ≤ 23)

Using a binomial probability calculator or formula, we find that P(X > 23) ≈ 0.0072.

The probability that more than 23 of the sampled high school graduates enroll in college is approximately 0.0072 or 0.72%, which is less than the 5% threshold commonly used to define unusual events.

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PLEASE HELP AS SOON AS POSSIBLE

Answers

The type and degree of association in the scatter plot and what it means is: A. As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.

What is a positive correlation?

In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

A positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation or strong linear association between the x-values (time practicing in minutes) and y-values (points scored) because they both increase simultaneously.

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Help pleaseeeeeeeeeeeeee

Answers

Answer: f(8) = 620.6

Step-by-step explanation:

To solve, you must first use substitution, and replace the x value in the given function, with 8.

[tex]f(8)=\frac{750}{1 + 74e^{-0.734(8)} }[/tex]

Next you follow PEMDAS to solve the rest of the equation to find f(8).

What is PEMDAS?

PEMDAS is the order of operations for mathematical expressions involving more than one operation.

You solve in the following order

P = ParenthesisE = ExponentsM = MultiplicationD = DivisionA = AdditionS = Subtraction

In this case our next step is deal with the exponents.

And by doing so, you will be multiplying -0.734 by 8

[tex]f(8)=\frac{750}{1 + 74e^{-5.872} }[/tex]

And typical with exponents we would raise the number or variable given to the power of the exponent.

However we have a continuous number in this case, which is e.

What is e?

e is a mathematical constant approximately equal to 2.71828

We can now use a calculator to find what e (2.71....) is when raise to the exponent -5.872. Which results to 0.002817 (0.0028172332293320237716146943697).

When continuing to use numbers in calculators, don't use the rounded or shortened of the full number. Make sure to use the all of the numbers (given in the calculator) to its full extent to maintain accuracy.

[tex]f(8)=\frac{750}{1 + 74(0.002817) }[/tex]

Now multiply 74 and 0.002817.... (use the full number to multiply (0.0028172332293320237716146943697)). The product is (0.2084752589705697590994873833578).

[tex]f(8)=\frac{750}{1 + 0.2084 }[/tex]

Now lets add 1 + 0.2084.... and you get 1.2084

[tex]f(8)=\frac{750}{1.2084 }[/tex]

Last you need to divide:

and you get that

f(8) = 620.6167

Now lets go back to the question, and we see that is says for you to round your answer to the nearest tenth.

so your final answer is:

f(8) = 620.6

find the absolute valve of 1 1/2 - 2/31

Answers

Answer: To find the absolute value of the expression 1 1/2 - 2/31, we first need to convert the mixed number 1 1/2 into an improper fraction.

1 1/2 can be written as (2 * 1 + 1) / 2, which is equal to 3/2.

Now we can subtract 2/31 from 3/2:

3/2 - 2/31 = (3 * 31 - 2 * 2) / (2 * 31) = (93 - 4) / 62 = 89/62.

The absolute value of a fraction is the positive value without considering its sign. So, the absolute value of 89/62 is 89/62.

Therefore, the absolute value of 1 1/2 - 2/31 is 89/62.

Reduce this fraction: 5/25x

Answers

Answer:

1/5x

Step-by-step explanation:

1/5x

A can of corn has a diameter of 14 cm and is 18.2 cm tall. How much metal is required to make the can?

Answers

Answer:

1108.67 square centimeters

Step-by-step explanation:

Surface Area = 2πr² + 2πrh

Radius = diameter / 2 = 14 cm / 2 = 7 cm

Surface Area = 2π(7 cm)² + 2π(7 cm)(18.2 cm)

Surface Area ≈ 2π(49 cm²) + 2π(127.4 cm²)

Surface Area ≈ 307.86 cm² + 800.81 cm²

Surface Area ≈ 1108.67 cm²

Therefore, approximately 1108.67 square centimeters of metal are required to make the can.

What is the equation for circumference?

Answers

Answer: c=2(pi)(r)

Step-by-step explanation:

C = circumference

\pi = the constant pi

r = radius of the circle

For the following equations find 1) the general form for all solutions 2) the solutions on the interval (pi/2)<=θ<3pi in terms of pi.
cscθ=2

Answers

1) The equation cscθ = 2 has a general form of θ = π/6 + 2πn, where n is an integer, representing all possible solutions.

2) The solutions for the equation cscθ = 2 on the interval (π/2) ≤ θ < 3π can be expressed as θ = π/6, (7π/6), (13π/6), (19π/6), and so on, where each term is a multiple of π/6 added to the previous solution.

To find the solutions of the equation cscθ = 2 on the interval (π/2) ≤ θ < 3π, we'll follow these steps:

Step 1: Rewrite the equation using the reciprocal identity for sine:

sinθ = 1/cscθ

Step 2: Substitute the value for cscθ:

sinθ = 1/2

Step 3: Find the solutions in the interval (π/2) ≤ θ < 3π for which sine is equal to 1/2. We know that sine is positive in the first and second quadrants.

In the first quadrant, the reference angle with a positive sine of 1/2 is π/6. The angle θ can be expressed as:

θ = π/6 + 2πn, where n is an integer.

In the second quadrant, the sine is also positive, but the reference angle is (π - π/6) = 5π/6. The angle θ in the second quadrant can be expressed as:

θ = π - (5π/6) + 2πn

  =  π/6 + 2πn, where n is an integer.

Step 4: Combine the solutions from the first and second quadrants.

θ = π/6 + 2πn, where n is an integer.

Step 5: Narrow down the solutions to the given interval.

Within the interval (π/2) ≤ θ < 3π, we can substitute n = 0, 1, 2, ... as follows:

θ = π/6, (π/6) + 2π, (π/6) + 4π, ...

Therefore, the solutions on the interval (π/2) ≤ θ < 3π in terms of π are:

θ = π/6, (7π/6), (13π/6), (19π/6), ...

In general form, the solutions can be expressed as:

θ = π/6 + 2πn, where n is an integer.

Hence, the general form for all solutions of the equation cscθ = 2 is θ = π/6 + 2πn.

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Insert<,>, or between the given pair of numbers to make a true statement.
|-38|
- (-38)

Answers

Both |-38| and -(-38) are equal to 38, the correct symbol to insert between the pair of numbers is "=" (equals). Hence, the true statement is: |-38| = -(-38)

To determine the relationship between |-38| and -(-38),

let's evaluate each expression separately:

|-38| = 38 (since the absolute value of -38 is equal to 38)

-(-38) = 38 (since negating a negative number results in a positive number)

Therefore, |-38| = -(-38) = 38.

Since both |-38| and -(-38) are equal to 38, the correct symbol to insert between the pair of numbers is "=" (equals).

Hence, the true statement is:

|-38| = -(-38)

It's important to note that the absolute value function (denoted by | |) always yields a non-negative value, regardless of the sign of the number within the absolute value brackets.

In this case, |-38| evaluates to 38, and the negation of -38 also evaluates to 38, resulting in an equality between the two expressions.

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Use the parabola tool to graph the quadratic function f(x)=−(x−2)2+4.

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

The vertex is (2, 4) and (3, 3)

To graph the quadratic function

[tex]f(x) = -(x - 2)^2 + 4[/tex],

we'll first identify the vertex and then plot a second point on the parabola.

The vertex form of a quadratic function is given by

[tex]f(x) = a(x - h)^2 + k[/tex],

where (h, k) represents the vertex of the parabola.

Comparing the given function

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

to the vertex form, we can identify that the vertex is located at (2, 4).

Now, let's plot the vertex (2, 4) on a coordinate plane and find another point on the parabola.

We can choose a value for x and calculate the corresponding y-coordinate using the function.

Let's choose x = 3.

Substituting this value into the function, we get:

[tex]f(3) = -(3 - 2)^2 + 4[/tex]

[tex]= -(1)^2 + 4[/tex]

[tex]= -1 + 4[/tex]

[tex]= 3[/tex]

So, when x = 3, y = 3.

Now we have two points: the vertex (2, 4) and (3, 3).

Let's plot them on a coordinate plane and draw the parabola:

   |

   |

   |

   |     *

   |          *

   |

   |_______________

        2  3  4

In the graph, the vertex is denoted by '*' and the second point is marked as '.'.

The parabola opens downward because the coefficient of (x - 2)^2 is negative.

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Using Pythagoras' theorem, calculate the length of XY. Give your answer in centimetres (cm) to 1 d.p. 16 cm X Z Y 5 cm Not drawn accurately​

Answers

The length of XY (height) is approximately 15.2 cm to 1 decimal place, according to Pythagoras' theorem.

To calculate the length of XY (height) using Pythagoras' theorem, we can use the formula:

[tex]\[XY = \sqrt{XZ^2 - ZY^2}\][/tex]

Given that XZ = 16 cm (hypotenuse) and ZY = 5 cm (base), we can substitute these values into the formula:

[tex]\[XY = \sqrt{16^2 - 5^2} = \sqrt{256 - 25} = \sqrt{231} \approx 15.2 \text{ cm}\][/tex]

Therefore, the length of XY (height) is approximately 15.2 cm to 1 decimal place.

When using Pythagoras' theorem, it is essential to ensure that you are working with a right-angled triangle. This means one angle should be 90 degrees. Identify the lengths of the two sides involved: the base and the perpendicular, or the hypotenuse. Apply the theorem correctly by squaring the lengths of the base and perpendicular sides, then summing them. The resulting sum should equal the square of the hypotenuse. Finally, take the square root of this sum to find the length of the missing side. Remember to round the answer to the appropriate decimal place based on the given precision. Double-checking these steps will help ensure accurate calculations using Pythagoras' theorem.

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how will the solution of y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3

Answers

When the inequality signs in the equations are reversed, the solution to the system of inequalities will change. In the original system, y > 2x + 2/3 and y < 2x + 1/3, the solution represents the region between two lines.

If we reverse the inequality signs to y < 2x + 2/3 and y > 2x + 1/3, the solution will now represent the region outside the lines. This means that the solution will be the area not covered by the lines themselves.

In summary, reversing the inequality signs in the equations will change the solution from the region between the lines to the region outside the lines.

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What is six-eighths times five?

Your answer should be in mixed number form.

one and ten-thirtieths
three and six-eighths
six and four-sixths
nine and three-fifths

Answers

six-eighths times five is equal to nine and three-fifths which can also be expressed as 3 3/5. This is the final answer.I hope this helps. Let me know if you have any other questions!

To solve the expression six-eighths times five, we will first convert six-eighths into a fraction. To convert it into a fraction, we need to simplify it by dividing both the numerator and denominator by their greatest common factor (GCF) which is 2. This gives us the reduced fraction of three-fourths.So, six-eighths is equal to three-fourths. Now we can substitute this in the expression and multiply it by five.3/4 x 5 = 15/4We can convert this improper fraction into a mixed number by dividing the numerator (15) by the denominator (4). When we divide 15 by 4, we get a quotient of 3 and a remainder of 3. We then express the remainder as a fraction over the denominator. This gives us a mixed number of 3 and 3/4.

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I’m super stumped plsss help

Answers

Answer:

Each mark on the top of the number line increases by 70, so the second mark is 140. Each mark on the bottom number increases by 20%. So 40% of 350 is 140.

Step-by-step explanation:

We can see that the number line is divided into 5 equal parts on both the top and bottom.

Let's do the bottom part of the number line first.We can divide 100 by 5 to get what each segment of the total number line is. 100/5=20. Each segment of the bottom number line is 20%. The rest of the bottom number line is adding by 20 until we have reached 100. 20%, 40%, 60%, 80%, 100%.

For the top: Having the bottom part done, we know that each small segment is 20%. We can multiply 350 (the total) by 0.2 which gives us 20% of 350. 350x0.2=70. Each part of the line segment for the top will increase by 70. You can keep adding 70 to each segment, which will fill out the number line just the same. But for more explanation, lets continue filling it out step by step. Now, we can multiply 350 by 0.4 (40%). 350x0.4=140 (part of your final answer). Continue doing so for the rest. An important thing to notice is that the numbers we are multiplying 350 by are all matching the percents that should be filled in at the bottom. 350x0.6=210. That's the third mark. Next, 350x0.8=280. That's the fourth mark. Now, we have 350, which is 100%.  

Also, when you're not asked to do a double number line, you can divide the part by the total. 140/350=0.4. 0.4=40%.

Hope this helped.

The gradient of a line passes through the points a (-3, -8) and H(x,-4). Find the value of x​

Answers

The value of x can be any real number.

To find the value of x when the gradient of a line passes through points A(-3, -8) and H(x, -4), we can use the formula for calculating the gradient (slope) of a line:

Gradient = (change in y) / (change in x)

Given that the gradient is the same between points A and H, we can set up the following equation:

(-8 - (-4)) / (-3 - x) = (change in y) / (change in x)

Simplifying the equation, we have:

(-8 + 4) / (-3 - x) = (-4 - (-8)) / (x - (-3))

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

To eliminate the fractions, we can cross-multiply:

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

Simplifying further, we have:

-4x - 12 = -12 - 4x

Rearranging the terms, we get:

-4x + 4x = -12 + 12

0 = 0

The equation simplifies to 0 = 0, which means that the value of x can be any real number. In other words, there are infinitely many possible values of x for which the gradient of the line passing through points A and H remains the same.

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Are quadrilaterals ABCD and EFGH similar?

Answers

Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 1, y + 3) and a dilation by the scale factor of 3 from point D′ map quadrilateral ABCD onto EFGH.

What are quadrilaterals?

The properties of quadrilaterals are;

Number of sides is equal to fourNumber of vertices  is equal to fourNumber of diagonals is twoSum of all interior angles is equal to 360 degrees

From the information given, we can see that;

ABCD and EFGH are similar because a translation of (x + 1, y + 3) and a dilation by the scale factor of 3

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Please help me solve for x as soon as possible.

Answers

The value of x in the secant line using the Intersecting theorem is 10.

What is the value of x?

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the diagram:

First sectant line segment = ( x + 6 )

External segement of the first secant line = 6

Second sectant line segment = ( 46 + 2 ) = 48

External segement of the second secant line = 2

Now, using the Intersecting secants theorem:

6 × ( x + 6 ) = 2 × 48

Solve for x:

6x + 36 = 96

6x = 96 - 36

6x = 60

x = 60/6

x = 10

Therefore, the value of x is 10.

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If
m



=
5
4

m
GT

=54

and
m



=
16
0

m
YC

=160

, find
m


m∠W.

Answers

Answer:

∠ W = 53°

Step-by-step explanation:

the measure of the secant- secant angle W is half the difference of the measures of the intercepted arcs , that is

∠ W = [tex]\frac{1}{2}[/tex] (YC - GT) = [tex]\frac{1}{2}[/tex] (160 - 54)° = [tex]\frac{1}{2}[/tex] × 106° = 53°

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