the formula for the area of a circle is a=πr²· if r =7 inches and π =3.14 what is the area of the circle

According to the problem,The area of the figure is approximately 34 square units.

A square is a four-sided plane figure where all sides are equal length and all angles are right angles. It is a two-dimensional shape with four equal-length sides and four equal angles of 90°. Squares are often used in designs and architecture, and are an important part of Euclidean geometry. They are also found in nature, such as in a honeycomb, in a checkerboard pattern, and in tessellations.

To calculate this, we need to calculate the area of the square and the area of the circle's segment. The side of the square is 4 units, so the area of the square is 4 x 4 = 16 square units. The radius of the circle is also 4 units, so the area of the circle's segment is (1/2)πr^2, which is (1/2)π(4^2) = 16π/2 = 16 x 3.14/2 = 24.96 square units.

Therefore, the area of the figure is 16 + 24.96 = 40.96 square units, which is approximately 34 square units to the nearest whole number.

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Answer:

the answer is 251.33

Step-by-step explanation:

PI*4^2*5=251.33

a) The expectation of the number of questions she would answer correctly is 21 questions. b)  If she answered a question on the exam correctly,  the probability it was just because she guessed is 7.89%.

a. If the exam has a total of 30 questions on it, we would expect the student to answer correctly 0.7 * 30 = 21 questions.

b. If she answered a question on the exam correctly, the probability it was just because she guessed is 0.3 * (1/5) = 0.06. This is because there is a 30% chance she did not know the answer and a 1/5 chance she guessed the correct answer.

To find the overall probability of answering a question correctly, we can use the law of total probability:

P(correct) = P(knows answer) * P(correct | knows answer) + P(does not know answer) * P(correct | does not know answer)
= 0.7 * 1 + 0.3 * (1/5)
= 0.76

Therefore, the probability that she answered a question correctly just because she guessed is 0.06 / 0.76 = 0.0789, or approximately 7.89%.

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The four points on the lemniscate where the tangent is horizontal are (0, ±a/sqrt(2)) and (±sqrt(a^2 - x^2), ±sqrt(a^2 - x^2)), where x is a solution of the equation x(x^2 + y^2 - 2a^2) = 0

Explanation: The lemniscate is given by the equation (x^2 + y^2)^2 = 2a^2(x^2 - y^2), where a is a positive constant. To find the points on the lemniscate where the tangent is horizontal, we differentiate this equation with respect to x:

d/dx [(x^2 + y^2)^2] = d/dx [2a^2(x^2 - y^2)]

2(x^2 + y^2)(2x + 2y dy/dx) = 4a^2x

To find the values of x where the tangent is horizontal, we set the derivative dy/dx equal to zero, since a horizontal tangent has zero slope. This gives:

2(x^2 + y^2)(2x) = 4a^2x

(x^2 + y^2)(2x) = 2a^2x

x(x^2 + y^2 - 2a^2) = 0

Thus, we have two possible values of x: x = 0 and x^2 + y^2 = 2a^2. To obtain the corresponding values of y, we substitute these values of x into the equation of the lemniscate:

When x = 0, we have y = ±a/sqrt(2), corresponding to the two points (0, ±a/sqrt(2)) on the lemniscate where the tangent is horizontal.

When x^2 + y^2 = 2a^2, we have y = ±sqrt(2a^2 - x^2), corresponding to the two pairs of points on the lemniscate where the tangent is horizontal: (±sqrt(a^2 - x^2), sqrt(a^2 - x^2)) and (±sqrt(a^2 - x^2), -sqrt(a^2 - x^2)).

Therefore, the four points on the lemniscate where the tangent is horizontal are (0, ±a/sqrt(2)) and (±sqrt(a^2 - x^2), ±sqrt(a^2 - x^2)), where x is a solution of the equation x(x^2 + y^2 - 2a^2) = 0.

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Answer:

1144

Step-by-step explanation:

100 + 98 + 96 +.... + 78+76 =

(12-0)/2 (176)  

(6.5) (176) = 1144

The sum of the series will be 1068.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

We have to rewrite the series as the sum.

A series in mathematics is the sum of a list of numbers that are generated according to some pattern.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

The terms of this series can be calculated by calculating the value of the function at different values of i.

The series is as follows -

100 + 98 + 96 +.... + 78+76

This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -

\(S = \frac{n}{2} \times {2a + (n-1)d}\)

S = \(\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22]\)

S = 6 x 178 = 1068

The sum of the series will be 1068.

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This statement best illustrates money used as a medium of exchange. In this scenario, the individual goes to the store and exchanges $68 for a pair of jeans. Money serves as a medium of exchange when it is used to facilitate transactions between buyers and sellers. In this case, the buyer wants a pair of jeans, and the seller wants to sell them for $68. Without money, they would have to engage in bartering, which can be cumbersome and inefficient. Money makes the transaction smoother and allows both parties to get what they want. Overall, this example demonstrates how money is an essential tool for facilitating transactions in our modern economy.
Hi! Your question is about the function of money as illustrated by the example of paying $68 for a pair of jeans. This statement best illustrates money used as a medium of exchange.

In this scenario, money is being used as a medium of exchange because it is facilitating the transaction between you and the store. Instead of using barter or trading goods and services directly, you use money to acquire the pair of jeans. This makes transactions more efficient and convenient since it eliminates the need for a double coincidence of wants, which is when two parties each have something the other wants. As a medium of exchange, money serves as a universally accepted means to buy and sell goods and services, like your jeans purchase at the store.

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The given differential equation y x²y² = x² is a nonlinear and not separable differential equation, which corresponds to option (D).

A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In this equation, the term x²y² makes it nonlinear.

A separable differential equation can be written in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. However, in the given equation, we cannot separate the variables y and x to obtain such a form.

To solve this particular differential equation, one approach is to rewrite it in a more manageable form. Let's rearrange the terms:

x² = y/(x²y²)

Now, we can multiply both sides by (x²y²) to eliminate the denominator:

x²(x²y²) = y

This equation is still nonlinear but can be used to find a particular solution for y given a specific initial condition.

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a. The linear equation is given by: g + s + b = 104.

b. The relationship between the number of silver to bronze medals in an equation of two unknowns is of: s + b = 56.

c. The numbers of each medals are given as follows:

The variables to the system of equations are given as follows:

They earned a total of 104 medals, hence the linear equation is of:

g + s + b = 104.

For item b, we have that g = 46, hence the relationship between the number of silver and the number of bronze medals is of:

46 + s + b = 104

s + b = 56.

The number of silver and bronze medals was the same, hence:

s = b

b + b = 56.

2b = 56

b = 28.

s = 28.

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A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds

What is endurance race?

A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.

The given table is attached below.

The number of laps in the range 82 to 84 seconds = 1

The number of laps in the range 84 to 86 seconds = 4

The number of laps in the range 86 to 88 seconds = 2

The number of laps in the range 88 to 90 seconds = 4

The number of laps in the range 90 to 92 seconds = 6

The number of laps in the range 92 to 94 seconds = 5

The number of laps in the range 94 to 96 seconds = 2

The number of laps in the range 96 to 98 seconds = 0

Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;

A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.

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Answer:A

Step-by-step explanation:

Answer:

He added $25 to the contents of his wallet.

Step-by-step explanation:

Here's what's happening, symbolically:

$6 + m = $31, or m = $25.  Jake added $25 (represented by m) to the contents of his wallet.

The three equations from the options are y^2-5y=750 , 750-y(y-5)=0 , (y+25)(y-30)=0

Quadratic Equation: A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex

it is given that area of  rectangular room is 750 square feet

A=750 square feet

The width of the room is 5 feet less than the length of the room

let length be y and width is 5 less than the length which is y-5

we know area of rectangle is ,A= 750=l x b= (y)(y-5)

which gives, (y)(y-5)=750 or 750-(y)(y-5)=0

                   y^2-5y=750

                   y^2-30y+25y-750=0

                  y(y-30)+25(y-30)=0

                  (y+25)(y-30)=0

                  y+25=0 and y-30=0

      where y=-25 and y=30

the three equations from the options are y^2-5y=750 , 750-y(y-5)=0 , (y+25)(y-30)=0

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The measure of the acute angles are 62° and 28° .

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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Start writing an expression that represents the balance of the account after the withdrawal each week

then, complete the inequality taking into account the conditions of leaving a minimum of $400

solve the inequality

Answer:

True!

Step-by-step explanation:

This is true because interest rates may be used when you are taking out a loan!

For example, you are taking a loan to buy a house. The company says that they are charging 1% interest rate per month. You are adding that 1%

I hope this makes sense!

Answer:

This equation have no solution.

Step-by-step explanation:

1) Simplify 4/2 to 2 because 4 divided by 2 is 2.

\(2 + 22 = 38\)

2) Simplify 2 + 22 to 24.

\(24 = 38\)

3) Since 24=38 is false, there is no solution.

\(no \: solution\)

Therefor, this equation have no solution.

a. The required linear equation is given by y = 1.5 d + 8.

b. The height of the plant after 20 days will be 38 cm.

We are given:

Bre is tracking the progress of her plant's growth.

Today the plant is 8 cm high.

The plant grows 1.5 cm per day.

a.

Let the number of days be d.

So,

The linear equation is given by;

y = 1.5 d + 8

b.

Substitute the value of d = 20 in the given equation we will get the:

y = 1.5 * 20 + 8

y = 30 + 8

y = 38 cm

So, the height of the plant after 20 days will be 38 cm.

Thus,

a. The required linear equation is given by y = 1.5 d + 8.

b. The height of the plant after 20 days will be 38 cm.

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A simple form of the equation of a line into slope-intercept form is y = -x +8

What is the slope-intercept form?

One method for expressing a linear equation is in the slope-intercept form. Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form.

The slope-intercept form of a line is given by

y = mx+b where m is the slope and b is the y-intercept.

4x + 4y = -32

Subtract 4x from each side

4x-4x + 4y =-4x -32

4y = -4x -32

Divide each side by 4

4y/4 = -4x/4 -32/-4

y = -x +8

The slope is -1 and the y-intercept is 8.

Hence, the simple form of the equation of a line into slope-intercept form is y = -x +8.

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Answer:

5.

A) 1:2

6.

D) 9 min

Plz make brainlest, THESE ARE THE CORRECT ANSWERRRRSS!

Step-by-step explanation:

5. 12:24

reduce to get 1:2

6. 225/25= 9 min

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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The equivalent expression is  -1.9b + 7.8.

There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Combine similar phrases now:

The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.

When we combine the term b's coefficient, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

By condensing the equation, we obtain

= (- 1.9) +b + 7.8

= −1.9b + 7.8

There is a condensed equivalent formula of -1.9b + 7.8.

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The other x-intercept of the given ellipse cannot be determined with the information provided. The equation of the ellipse depends on the lengths of the semi-major and semi-minor axes, which are not specified. Therefore, there are multiple ellipses that can satisfy the given conditions, resulting in different values for the other x-intercept.

To find the x-intercepts of the ellipse, we need to determine the equation of the ellipse first. The standard form equation of an ellipse with foci at  (h, k ± c) and x-intercepts (h ± a, k) is given by:

((x - h)² / a²) + ((y - k)² / b²) = 1

Where (h, k) represents the center of the ellipse, a is the semi-major axis length, b is the semi-minor axis length, and c represents the distance from the center to each focus.

In this case, the center of the ellipse is at (h, k) = (1.5, 1), and the distance between the center and each focus is given by c = 2.

Substituting these values into the equation, we have:

((x - 1.5)² / a²) + ((y - 1)² / b²) = 1

Now, since one of the x-intercepts is at the origin (0, 0), we can substitute these values into the equation to solve for a and b:

((0 - 1.5)² / a²) + ((0 - 1)² / b²) = 1

(2.25 / a²) + (1 / b²) = 1

Simplifying this equation, we get:

2.25 / a² + 1 / b² = 1

Now, we need to find the other x-intercept, which means finding the value of x when y is 0. Substituting y = 0 into the equation, we have:

((x - 1.5)² / a²) + ((0 - 1)² / b²) = 1

(x - 1.5)² / a² + 1 / b² = 1

Since one of the x-intercepts is at the origin, we know that x = 0 satisfies this equation:

(-1.5)² / a² + 1 / b² = 1

2.25 / a² + 1 / b² = 1

Now we have two equations:

2.25 / a² + 1 / b² = 1  (Equation 1)

2.25 / a² + 1 / b² = 1 (Equation 2)

Both equations are the same, so we can combine them:

2.25 / a² + 1 / b² = 1

Since both equations are identical, there are infinite solutions for a and b that satisfy this equation. Therefore, there is no unique value for the other x-intercept of the ellipse.

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The complete question is :

An ellipse has foci at (0,2) and (3,0). The ellipse has two x-intercepts, one of which is the origin. What is the other x-intercept?

Journal entries for Southeastern College as a public university:

1. Donation received for capital addition:

Restricted Cash - Capital Additions Dr. $502,000

Donation Revenue Cr. $502,000

2. Contribution to the permanent endowment:

Cash Dr. $210,000

Permanently Restricted Net Assets Cr. $210,000

3. Interest and dividends received on endowment investments:

Restricted Cash - Scholarships Dr. $50,000

Investment Income Cr. $50,000

4. Increase in fair value of investments:

Investment Gain  Dr. $7,100

Unrestricted Net Assets  Cr. $7,100

To record the transactions for Southeastern College as a public university, the following journal entries are made:

1. Recording the donation received for capital addition:

Restricted Cash - Capital Additions  Dr. $502,000

Donation Revenue Cr. $502,000

The restricted cash is increased by $502,000, representing the additional donation received for capital additions. The corresponding revenue account is credited.

2. Recording the contribution to the permanent endowment:

Cash Dr. $210,000

Permanently Restricted Net Assets Cr. $210,000

The cash received from the alum is debited, and the permanently restricted net assets (part of the endowment) are credited.

3. Recording interest and dividends received on endowment investments:

Restricted Cash - Scholarships Dr. $50,000

Investment Income Cr. $50,000

The interest and dividends received on the endowment investments are debited to restricted cash for scholarships, and the investment income account is credited.

4. Recording the increase in fair value of investments:

Investment Gain  Dr. $7,100

Unrestricted Net Assets  Cr. $7,100

The increase in the fair value of the investments is recorded as an investment gain. The unrestricted net assets account is credited, as gains or losses from changes in fair value are not distributed and remain in the endowment.

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No , the equality x + x·y + x·y·z = x does not hold when x, y, and z are boolean variables.

In boolean algebra, the "+" operator represents logical OR, and the "·" operator represents logical AND. Let's analyze the equation x + x·y + x·y·z = x. The term x·y can only be true (1) if both x and y are true (1). Similarly, x·y·z can only be true (1) if x, y, and z are all true (1). Therefore, the equation can be simplified to x + (x·y) + (x·y·z) = x.

If we consider the case where x = 1, y = 0, and z = 1, the equation becomes 1 + (1·0) + (1·0·1) = 1. However, evaluating the equation, we get 1 + 0 + 0 = 1, which is not equalequal to x. This example shows that the equality does not hold, indicating that the answer is option (b) "no."

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Answer:

acute is one of the i hope this helps

The displacement of the object between t=0 and t=1 second is 5.66 m.

The displacement of the object between t=0 and t=1 second is calculated as follows;

The given equation of the object's motion;

x = 4 cos (πt  +  π/4)

where;

at a time, t = 0 second, the displacement of the object is calculated as;

x = 4 cos (πt  +  π/4)

x = 4 cos (0 + π/4)

x = 4 cos (π/4)

x = 2.83 m

at time t = 1 second, the displacement of the object is calculated as;

x = 4 cos (π  + π/4)

x = 4 cos (5π/4)

x = -2.83 m

The displacement of the object between the time given;

x = 2.83 m - ( - 2.83 m )

x = 5.66 m

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Answer:

60 to 90 feet tall

Step-by-step explanation:

i just looked it up

1. (A)  Section titles  (lines starting with %% followed by a space and then a title).

2. (B)  Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

The source of the section headers in the resulting document when publishing a script from the MATLAB Editor is:

a. Section titles (lines starting with %% followed by a space and then a title).

The statement that is not true about the purpose of code in the MATLAB Editor is:

b. Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. The commands that return a matrix of the same size as x, given a non-scalar matrix X, are:

a. mean(x)

b. sin(x)

c. log(x)

d. sum(x)

e. std(x)

f. sqrt(x)

All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

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