Pls answer!! reward is a lot of points. Question is "7/4 - (- 1/6)"

Step-by-step explanation:

The circumference of a circle can be found using the formula:

C = πd

where C represents the circumference and d represents the diameter of the circle.

Given that the diameter of the circle is 4 feet, we can substitute this value into the formula:

C = π * 4

Therefore, the circumference of the circle is 4π feet.

The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

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

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

For more such questions on equation of a line, click on:

https://brainly.com/question/18831322

#SPJ8

The number of subsets for the set in this problem is given as follows:

16 subsets.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is given as follows:

{C, D, E, F}.

Hence the cardinality of the set is given as follows:

n = 4.

Then the number of subsets is given as follows:

[tex]2^4 = 16[/tex]

More can be learned about the subsets of a set at brainly.com/question/13458417

#SPJ1

Answer:

  (a)  Use the distance formula to find the length of each side, and then add the lengths.

Step-by-step explanation:

You want to know a suitable strategy for finding the perimeter of a quadrilateral when the coordinates of its vertices are known.

The perimeter of a figure is the sum of its side lengths. When the coordinates of the ends of a side segment are known, the length of that segment can be found using the distance formula.

This should make it obvious that a suitable strategy for finding the perimeter is to find the length of each side and add the lengths.

__

Additional comment

The slope is irrelevant when the perimeter is what you want.

The slope can be relevant if you're trying to prove a quadrilateral is a parallelogram or rectangle (or something else with parallel sides). (There are easier ways than using the slope.)

Multiplying side lengths will be relevant if you want the area of a rectangle. The product has no relation to the perimeter.

<95141404393>

The domain of the function y = 3 tan(2/3x) is all real numbers except for x = (3n + ³/₂)π., where n is an integer.

The function is given as: y = 3 tan(2/3x)

The function above is defined for all values of x except where the tangent function is undefined. The tangent function is undefined at angles where the cosine is zero. In this case, the cosine is zero when 2/3x is equal to an odd multiple of π/2.

So we set (2/3)x equal to (2n + 1)π/2, where n is an integer:

(2/3)x = (2n + 1)π/2.

To solve for x, we multiply both sides by 3/2:

x = (3/2)(2n + 1)π/2.

x = (3n + ³/₂)π.

Therefore, the function is undefined when x is equal to (3n + 3/2)π, where n is an integer.

The domain of the function y = 3 tan(2/3x) is all real numbers except for x = (3n + ³/₂)π., where n is an integer.

Read more about https://brainly.com/question/10197594at:

#SPJ1

To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:

For such more question on equations

https://brainly.com/question/22688504

#SPJ8

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.

For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938

For New York: Ratio = 911,216 / 18.6 million = 0.049019

For Cairo: Ratio = 10,598 / 19.1 million = 0.000554

For Beijing: Ratio = 959,611 / 21.2 million = 0.045270

For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234

To calculate the owners per 100, we multiply the ratio by 100.

For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)

For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)

For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)

For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)

For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)

Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:

Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7

New York: Ratio = 0.049019, Owners per 100 = 4.9

Cairo: Ratio = 0.000554, Owners per 100 = 0.1

Beijing: Ratio = 0.045270, Owners per 100 = 4.5

Tokyo: Ratio = 0.064234, Owners per 100 = 6.4

For such more question on Ratio

https://brainly.com/question/12024093

#SPJ8

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

For such more question on gallons

https://brainly.com/question/28274339

#SPJ8

The probability that a person will purchase no more than one costume is given as follows:

93%.

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

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:

187 + 228 + 29 = 444.

Only 29 people purchased more than one costume, hence the probability of at most one costume is calculated as follows:

(444 - 29)/444 = 0.93 = 93%.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

for more such question on matrix visit

https://brainly.com/question/2456804

#SPJ8

The angles formed by the transversal line r and the parallel lines s and t, have that:

A. ∠5 ≈ ∠7 {vertical angles}

B. ∠1 + ∠2 = 180° {angles on straight line}

C. ∠4 ≈ ∠8 {corresponding angles}

D. ∠6 + ∠7 = 180° {angles on straight line}

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.

A. The angles ∠5 and ∠7 are vertical angles as they are vertically opposite, so ∠5 = ∠7

B. The angles ∠1 and ∠2 angles on a straight line and their sum is equal to 180° so;

∠1 + ∠2 = 180°

C. The angles ∠4 and ∠8 are corresponding angles and are equal, so ∠4 = ∠8

D. The angles ∠6 and ∠7 angles on a straight line and their sum is equal to 180° so;

∠6 + ∠7 = 180°

Therefore, for the angles formed by the transversal line r and the parallel lines s and t, we have that:

A. ∠5 ≈ ∠7 {vertical angles}

B. ∠1 + ∠2 = 180° {angles on straight line}

C. ∠4 ≈ ∠8 {corresponding angles}

D. ∠6 + ∠7 = 180° {angles on straight line}

Read more about angles here:https://brainly.com/question/24607467

#SPJ1

Answer:

If you earn $50,000 a year and you max out your contribution to a 401(k) plan, you would contribute $19,500 (assuming you are under 50 years old). This means you would save $19,500 per year towards your retirement.

The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.

To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...

To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...

We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.

Using this pattern, we can determine the 9th and 10th arrangements as follows:

9th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

Therefore, the 9th arrangement will have 36 dots.

10th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Therefore, the 10th arrangement will have 45 dots.

Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.

If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.

For example, let's consider the 2nd and 3rd arrangements:

2nd arrangement: 3 dots

3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots

This pattern holds true for any two consecutive arrangements in the sequence.

for such more question on arrangement

https://brainly.com/question/28554042

#SPJ8

Answer: (C) 1/3

Step-by-step explanation:

Look at the base lengths. For A'B'C', the length is 2. For ABC, it is 6. The ratio of the length of A'B'C' to the length of ABC is 1/3. Thus the answer is C.

The volume of the new cone is 1,536π cubic inches.

To find the height of the cone, we can use the formula for the volume of a cone:

V = (1/3)πr²h

Given that the volume of the cone is 414.7 cubic inches and the radius is 6 inches, we can substitute these values into the formula and solve for h:

414.7 = (1/3)π(6)²h

414.7 = (1/3)π(36)h

414.7 = 12πh

h = 414.7 / (12π)

h ≈ 10.93 inches

Therefore, the height of the cone is approximately 10.93 inches when rounded to the nearest whole inch.

Next, let's calculate the volume of the new cone after doubling the radius to 12 inches and changing the height to 8 inches.

Using the same formula, we have:

V = (1/3)π(12)²(8)

V = (1/3)π(144)(8)

V = 1,536π

The redesigned cone has 1,536 cubic inches of capacity.

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

For more such question on algebric expression. visit :

https://brainly.com/question/4344214

#SPJ8

Let's arrange the steps for solving the expression using the order of operations (also known as PEMDAS/BODMAS):

Subtract: (42-13) = 29

Multiply: 4 × 3 = 12

Exponentiation: 5² = 25

Multiply: 8 × 3 = 24

Divide: 24 ÷ 29 (result from step 1) = 0.8276 (rounded to 4 decimal places)

Add: 0.8276 (result from step 5) + 25 (result from step 3) = 25.8276 (rounded to 4 decimal places)

Add: 25.8276 (result from step 6) + 12 (result from step 2) = 37.8276 (rounded to 4 decimal places)

The steps should be performed in the following order:

Subtract -> Multiply -> Exponentiation -> Multiply -> Divide -> Add -> Add

So the steps should be performed in this order to evaluate the expression correctly.

For more questions on: order of operations

https://brainly.com/question/27529825

#SPJ8  

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

for such more question on integers

https://brainly.com/question/22008756

#SPJ8

The distance between A and B based on the diagram is approximately 1,685.2 cm.

Hypotenuse = 1,920 cm

Adjacent = 920 cm

A and B = opposite

Hypotenuse² = adjacent² + opposite²

1920² = 920² + AB²

3,686,400 = 846,400 + AB²

3,686,400 - 846,400 = AB²

2,840,000 = AB²

find the square root of both sides

AB = √2,840,000

AB = 1685.229954635271

Approximately,

AB = 1,685.2 cm

Hence, distance between A and B is 1,685.2 cm.

Read more on Pythagoras theorem:

https://brainly.com/question/343682

#SPJ1

The transformation T maps the unit square to a figure with an area of 24 and a vertex at (5,3) which gives: T(x, y) = (6x + 5, 8y + 3).

To find a transformation T that maps the unit square to a figure with an area of 24 and a vertex at (5,3), we can use a combination of scaling and translation.

Let's denote the unit square as S, and the transformed figure as F.

To obtain a rectangle with an area of 48 and a vertex at (5,3), we can scale the unit square by multiplying the x-coordinates by 6 and the y-coordinates by 8, and then translate the scaled rectangle by adding (5,3) to the coordinates of each point.

Therefore, the transformation T can be expressed as:

T(x, y) = (6x + 5, 8y + 3)

Learn more about Transformation on:

https://brainly.com/question/4289712

#SPJ1

The expression which represents the quotient of the model is x² + 5x.

The correct answer choice is option B.

The quotient of a number is the number resulting from the division of one number by another.

There is one x²

There are 5 x

Hence, the quotient of the expression is x² + 5x

Read more on quotient:

https://brainly.com/question/629998

#SPJ1

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

Read more about Partial Differential Equations at: https://brainly.com/question/28099315

#SPJ1

Answer:

.6

Step-by-step explanation:

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

for similar questions on population.

https://brainly.com/question/30396931

#SPJ8

Answer:

[0,∞)

Step-by-step explanation:

The domain is just all the x values in the function. We can see in the graph that it starts at x=0 (inclusive per the filled in circle) and keeps going to the right forever (per the arrow at the end of the line). Therefore, x values for this function go from 0 to ∞.

thus, the domain is [0,∞)

Answer:

a)  ∩

Step-by-step explanation:

set A : {6,8,10,12}

set B : {5,6,7,8,9}

set C : {6,8}

A ∪ B = {6,8,10,12} ∪ {5,6,7,8,9} = {5,6,7,8,9,10,12} ≠ C

A ∩ B = {6,8,10,12} ∩ {5,6,7,8,9} = {6, 8} = C

Therfore{6,8,10,12} ∩ {5,6,7,8,9} = {6, 8}

Answer:

polynomial; left 3 right 1

Step-by-step explanation:

The type of function is a polynomial.

The parent function is translated by moving -2x^3 to the left 3 and right 1.

Answer:

The function is a quadratic function.

Series of transformations:

Step-by-step explanation:

A quadratic function is a polynomial function of degree 2 (the highest exponent of the variable is 2).

Therefore, the given equation, y = -2(x + 3)² + 1, represents a quadratic function as the term (x + 3)² indicates that the highest power of the x-variable is 2.

[tex]\hrulefill[/tex]

The parent function of a quadratic function is y = x².

To translate the parent function to produce the given equation, we need to apply this series of transformations:

1. Horizontal translation

When "a" is added to the x-variable, the graph is shifted "a" units to the left. Therefore, the addition of 3 inside the parentheses shifts the graph horizontally to the left by 3 units.

2. Vertical Stretch

The coefficient in front of the squared term (x + 3)² indicates a vertical stretch or compression. In this case, since the coefficient greater than 1, it stretches the graph vertically, making it narrower compared to the parent function.

3. Reflection

As the stretch coefficient is negative, the graph is reflected across the x-axis, meaning the parabola opens downwards.

4. Vertical translation

When "a" is added to the function, the graph is shifted "a" units up. Therefore, the addition of 1 to the function shifts the graph vertically up by 1 unit.

In summary, the series of transformations that maps the parent function to the given function is:

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

for such more question on linear equations

https://brainly.com/question/19803308

#SPJ8