16 can be written as:
O
A. 22

B. 44

c. 24
D. 82
E. 28

The area of the shaded region is 502.4 ft^2

The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.

It is given that inner diameter is 36 ft and width of the ring is 4 ft

We need to find the area of the shaded region

diameter of outer ring= d1=36+4+4 = 44 ft ,

diameter of inner ring= d2=36 ft,

r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft

Area of shaded region = Area of Outer circle - Area of inner circle

= π r1^2 - π r2^2

= π ( 22^2 - 18^2 )

= 3.14 * 160

= 502.4 ft^2

Hence the area of the shaded region is 502.4 ft^2

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The area of the shaded region is 502.4 sq. ft.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.

According to the question,

Diameter of inner circle = 36 ft.

Radius of inner circle = 36/2 ft. =18 ft.

As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.

Radius of outer circle = 22 ft.

Area of the shaded region = Area of outer circle - Area of inner circle

                                              = π(22)(22) - π(18)(18)

                                              = π(484 - 324)

                                              = 3.14 * 160

                                              = 502.4 sq. ft.

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Answer:

Step-by-step explanation:

The line has a positive slope and negative y-intercept.

This is only matched by a choice C

Take 2 points

Slope:-

\(\\ \sf\longmapsto m=\dfrac{1+3}{1}=4\)

Equation of line in point slope form

\(\\ \sf\longmapsto y-y_1=m(x-x_1)\)

\(\\ \sf\longmapsto y+3=4x\)

\(\\ \sf\longmapsto y=4x-3\)

Answer:

y= -2x + 3

Step-by-step explanation:

Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

Answer:

x = \(\frac{1}{3}\)

Step-by-step explanation:

\(\frac{1}{x} + \frac{1}{3x} = 4\) (Multiply everything by LCM)

\(3x*\frac{1}{x} + 3x*\frac{1}{3x}=3x*4\) (Simplify the fractions)

\(3+1=12x\\4=12x\\x=4/12\\x=\frac{1}{3}\)

Answer:

1. 10x+3

2. 20433

Step-by-step explanation:

For part 1:

3x+7x-28+31

=3x+7x+3

=10x+3

For part 2:

10x+3

=(10(2043))+3

=20433

The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.

Let the total amount of sources of nutrient you consumed daily be x miligrams.

According to the given question.

One-half cup of black beans provides 15 percent of the potassium.

Also, you get remaning nutrients from 2890 miligrams of other sources.

⇒ you get 85 percent of remaining nutrients from other sources.

So, we can say that

85 percent of x = 2890 miligrams

⇒ 85/100 × x = 2890 miligrams

⇒ x = (2890 × 100)/85

⇒ x = 3400

So, the total amount of source of nutrients is 3400.

Therefore,

The amount of potassium you should consume daily

= 15 percent of 3400

= (15/100) × 3400

= 15 × 34

= 510 miligrams

The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.

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Answer:

D) 80

Step-by-step explanation:

30 x 80 = 24

  100

30/100 = 24/80

30% = 24

24 is 30% of 80

Hopefully this helped! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

Answer:

16 cans per minute

Step-by-step explanation:

Its simple 80 divided by 5 is 16 so ever minute 16 cans are packed.

The ratio of the cans to minutes is 80 : 5 or 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign: between the numbers.

A machine can pack 80 cans in 5 minutes.

let's denote the number of cans with X and

Time with T

So we have to find the value of X : T

X = 80 and

T = 5 minutes

X : T = 80 : 5  or

X : T = 16 : 1   (divide by 5 on both sides)

It means the machine can pack 16 cans per minute.

Thus, the ratio of the cans to minutes is 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.

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The area of the square increasing with  56 cm²/s

Area or A = x²

where x represents one side of the square

The rate at which each side is increasing or dx/dt = 4 cm/s.

The area of the square is 49cm²

A = x²

x = √A

x = √49 = 7

Each side of the square or x = 7cm

We are trying to find the rate the area is changing, so dA/dt

A=x²

Take the derivative of the area equation with respect to time

dA/dt= 2x * dx/dt

Now plug in the values given to solve for dA/dt: x = 7 cm and dx/dt= 4 cm/s

2 (7) * (4) = 56 cm²/s

Therefore, the area of the square increasing with  56 cm²/s

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The equation also holds true for k+1. By mathematical induction, we have proved that the equation is true for all positive integers n.

To prove that 12−22+32−…+(−1)n−1n2=(−1)n−1n(n+1)2 whenever n is a positive integer using mathematical induction, we must first establish the base case.

When n=1, we have 1^2 = 1 and (-1)^(1-1) * 1 * (1+1) / 2 = 1. Therefore, the equation holds true for n=1.

Next, we assume that the equation holds true for some arbitrary positive integer k, meaning:

1^2 - 2^2 + 3^2 - ... + (-1)^(k-1) * k^2 = (-1)^(k-1) * k * (k+1) / 2

Now, we must prove that the equation also holds true for k+1:

1^2 - 2^2 + 3^2 - ... + (-1)^(k-1) * k^2 + (-1)^k * (k+1)^2 = (-1)^k * (k+1) * (k+2) / 2

Starting with the left side of the equation, we can substitute in the assumed equation for k:

(-1)^(k-1) * k * (k+1) / 2 + (-1)^k * (k+1)^2

Simplifying this expression:

(-1)^(k-1) * k * (k+1) / 2 - (k+1)^2 * (-1)^k

= (k+1) * [(-1)^(k-1) * k / 2 - (k+1) * (-1)^k]

= (k+1) * [(-1)^(k-1) * k / 2 + (k+1) * (-1)^{k+1}]

= (k+1) * [(-1)^(k-1) * k / 2 + (-1)^k * (k+1)]

= (k+1) * [(-1)^k * (k+1) / 2]

= (-1)^k * (k+1) * (k+2) / 2

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Answer:

6 and 102 = 62

119 and 23 = 38

96 and 51 = 33

28 and 87 = 65

Step-by-step explanation:

just did mine :D

Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Answer:

You have the right answer selected

Step-by-step explanation:

Answer:

You are correct.

Step-by-step explanation:

Distribute 16 to 3b to get 48b. Distribute 16 to 0.25 to get 4. Keep the subtraction and end up with 48b - 4.

The variation in the independent variable is 0.81%. Thus option C is correct option.

According to the statement

We have given that the coefficient of determination is .90, and we ahve to find the variation in the independent variable.

So, For this purpose, we know that the

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects.

And

We know that the

The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.

Due to this reason the variation in the independent variable is 0.81%.

So, The variation in the independent variable is 0.81%. Thus option C is correct option.

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The remaining distance Jada has to bike is 19/10 km.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Jada biked for 3.5 kilometers before stopping to adjust the helmet.

d₁ = 3/5 kilometer

Jada bikes another 1/2 kilometer and stopped to drink water.

d₂ = 1/2 kilometer

The total distance Jada has to bike is 3 kilometers.

The distance traveled by Jada is:

= d₁ + d₂

= 3/5 km + 1/2 km

Using LCM,

= ( 6 + 5 ) / 10

= 11/10 km

The distance remaining to cover is :

- 3 km - 11/10 km

= ( 30 - 11 ) / 10 km

= 19/10 km

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Answer:

Step-by-step explanation:

The correct answer is d. p1=p2=p3=p4=0.25.

In a multinomial experiment, the null hypothesis specifies the values of the population proportions for each category. Therefore, options (a), (b), and (c) cannot be the null hypothesis since they specify values for the population means, not the population proportions.

Option (d) specifies that all population proportions are equal to 0.25, which is a valid null hypothesis for a multinomial experiment with four categories.

Answer:

7x

Step-by-step explanation:

Hope this Helps

The equation of the linear line that best fit the given points is y = (7/8)x + 7/8.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The line passes through points (-1,0) and (7,7) will be the best fit as it is at the smallest distance between all points.

The linear function associated with the point (-1,0) and (7,7) will be as,

y - 0 = [(7 - 0)/(7 + 1)](x + 1)

y = (7/8)(x + 1)

y = (7/8)x + 7/8

Hence "y = (7/8)x + 7/8 is the equation of the linear line that best fits the provided points".

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Answer:

x = 200

Step-by-step explanation:

Given equation:

\(\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\)

Steps:

1. Substitute 15 as the value of y in the equation:

\(\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30\)

2. Add 10 to both sides:

\(\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40\)

3. Multiply both sides by 5 to isolate x:

\(\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200\)

4. Check your work:

\(\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark\)

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Hey there!

\( \boxed{\bold{\green{ x = 200}}} \)

\( \\ \)

Given expression :

\( \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } \)

1) Substitue 15 for \( \sf{\orange{y}} \) :

\( \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } \)

\( \\ \)

2) Solve for x :

\(\sf{ \frac{1}{5} \green{x} - 10= 30 } \)

⇢Add 10 to both sides of the equation :

\(\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

⇢Multiply both sides of the equation by 5:

\( \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}\)

\( \\ \)

3) Let's check our answer by replacing \( \green{x} \) with 200 and \( \orange{y} \) with 15 :

\( \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } \)

\( \\ \\ \)

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We can prove that the matrix A = [[sin θ, -cos θ], [cos θ, sin θ]] is invertible with an inverse of [[sin θ, cos θ], [-cos θ, sin θ]].

To show that the matrix A = [[sin θ, -cos θ], [cos θ, sin θ]] is invertible, we need to prove that its determinant is non-zero. The determinant of A can be calculated as follows:

det(A) = (sin θ * sin θ) - (-cos θ * cos θ)

= sin^2 θ + cos^2 θ

= 1

Since the determinant of A is equal to 1, which is non-zero, we can conclude that A is invertible.

To find the inverse of A, we can use the formula for the inverse of a 2x2 matrix:

A^(-1) = (1/det(A)) * adj(A)

The adjugate (adj(A)) of A is obtained by swapping the elements on the main diagonal and changing the sign of the elements off the main diagonal:

adj(A) = [[sin θ, cos θ], [-cos θ, sin θ]]

Therefore, the inverse of A is given by:

A^(-1) = (1/1) * [[sin θ, cos θ], [-cos θ, sin θ]]

= [[sin θ, cos θ], [-cos θ, sin θ]]

In summary, the matrix A = [[sin θ, -cos θ], [cos θ, sin θ]] is invertible with an inverse of [[sin θ, cos θ], [-cos θ, sin θ]].

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The quadrilateral FGHI is a parallelogram

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

F = (0, -6), G = (7, -4), H = (8, 4), I = (1, 2)

The lengths can be calculated as

Lengths = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the above as a guide, we have the following:

FG = √[(0 - 7)² + (-6 + 4)²] = √53

GH = √[(8 - 7)² + (4 + 4)²] = √65

HI = √[(8 - 1)² + (4 - 2)²] = √53

IF = √[(1 - 0)² + (2 + 6)²] = √65

For the slopes, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

FG = (-6 + 4)/(0 - 7) = 2/7

GH = (4 + 4)/(8 - 7) = 8

HI = (4 - 2)/(8 - 1) = 2/7

IF = (2 + 6)/(1 - 0) = 8

Based on the above computations, we have

Hence, the shape is a parallelogram

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Therefore, the three left cosets of h in z are: 0 + h = {x ∈ z | x ≡ 0 (mod 3)}, 1 + h = {x ∈ z | x ≡ 1 (mod 3)} and 2 + h = {x ∈ z | x ≡ 2 (mod 3)}.

Here, z denotes the set of all integers, and h = {0, 63, 66, 69, ...} is a subset of z.

To find the left cosets of h in z, we need to choose an integer a from z and then form the set of all integers of the form a + h, where a + h = {a + x | x ∈ h}.

For example, if we choose a = 5, then the left coset of h containing 5 is:

5 + h = {5 + x | x ∈ h} = {5, 68, 71, 74, ...}

To find all the left cosets of h, we can choose different values of a and repeat the process. However, we notice that all the elements of h have a common divisor of 3, since h contains 0 and all the other elements differ from 0 by a multiple of 3. Therefore, we can partition z into three sets:

z0 = {3n | n ∈ z} is the set of all integers that are multiples of 3.

z1 = {3n + 1 | n ∈ z} is the set of all integers that have a remainder of 1 when divided by 3.

z2 = {3n + 2 | n ∈ z} is the set of all integers that have a remainder of 2 when divided by 3.

We claim that each left coset of h in z belongs to exactly one of these sets. To see why, suppose that a + h and b + h are two left cosets of h in z. Then, for any x ∈ h, we have:

(a + x) - (b + x) = a - b

Since a - b is a fixed integer, it follows that either all the elements of a + h and b + h differ by the same integer (in which case a + h = b + h), or there are no common elements between a + h and b + h.

Now, we can compute the left coset of h containing 0, which is:

0 + h = {x ∈ z | x ≡ 0 (mod 3)}

This is because adding an element of h to 0 does not change its residue modulo 3. Therefore, the left coset of h containing 0 belongs to z0.

Next, we can choose an integer from z1 and compute its left coset. For example, if we choose a = 1, then:

1 + h = {x ∈ z | x ≡ 1 (mod 3)}

This left coset belongs to z1.

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The amount he had to pay if he have to purchase a laptop today that is the same value as the one he saw in the ad is $ 390.24.

Given that:-

Price of the laptop after 1 year = $ 400.

Inflation rate = 2.5 %

We have to find the amount he had to pay if he have to purchase a laptop today that is the same value as the one he saw in the ad.

Let the price he had to pay be x.

Hence, we can write,

x + (x*(2.5)*1)/100 = 400

x(1 + 1/40) = 400

x(41/40) = 400

x = 400*40/41 = $ 16000/41 = $ 390.24.

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