The radius of a circle is 8 feet. What is the area of a sector bounded by a 144° arc?

The computation illustrated shows that the numbers that can be used to get the sum of 42 will be 12 and 15.

It should be noted that the puzzle simply involves algebraic thinking. The goal is to find numbers that can be added together that will give 42.

From the information, it should be noted that 7 and 8 have been given. Therefore, this will be:

= 42 - (7 + 8)

= 42 - 15

= 27

Therefore, the numbers that can give 27 can be put in the box. An example is 12 and 15.

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The probability of the combined event that the next six days are all sunny is 1/4096

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

Probability that it is sunny = 1/4

Probability that it is cloudy = 3/4

Number of days = 6

The probability for all six days, it is sunny is represented as

Probability = Probability that it is sunny^Number of days

Substitute the known values in the above equation, so, we have the following representation

Probability = (1/4)⁶

Express as decimal

Probability = (0.25)⁶

Evaluate the exponent

Probability = 1/4096

Hence, the probability is 1/4096

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Rhonda I just got home from

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.

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The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

We have to given that;

The sequence is,

⇒ 3, 23, 123, 623, 3123, ...

Now, We can formulate;

⇒ 3 = 5 - 2

⇒ 23 = 5² - 2

⇒ 123 = 5³ - 2

⇒ 623 = 5⁴ - 2

Thus, The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

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Answer

1-right

2-not a triangle

3-acute

4-obtuse

5-right

6-obtuse

7-acute

Step-by-step explanation:

Answer:

$315

Explanation:

.04/12= 0.0033333...

.0033333...*15=0.05

.05+1(Because the number is supposed to be going up not down)=1.05

1.05*300=315

When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Answer:

America is correct

Step-by-step explanation:

it says 0,0 and then it would mean it wouldn't have any sugar in the pies

Answer:

No, America's wrong.

If you look on the graph, as the line increases you can see one pie needs around 3/4(not accurate). (0,0) is the origin point. No sugar is used, and no pie was made.

If Amelie worked alone, she would have worked for 4 hours.

We are going to be establishing mathematical relationships to solve this question.

Let t represent the time we are looking for

r to represent Ricardo's rate

a to represent Amelie's rate

we can then say that

from the first equation, we can agree that, r = 1/(t+8)

from the second we can also agree that, a = 1/t

If we substitute these two values in the third equation, we have

1 = {1/(t+8) + 1/t} 3, from this we have

t(t + 8) = 3t + 3(t+8)

t² + 8t = 3t + 3t + 24

t² + 8t = 6t + 24, if we collect like terms, we have

t² +8t -6t - 24 = 0

t² +2t -24 = 0,  if we factorize, we have

t² + 6t - 4t - 24 = 0

t(t+6) -4(t+6) = 0

(t+6) (t-4) = 0

t = 4 hours

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Answer:

1344 - 96 = 1248

If you want to check your answer the add 1248 + 96 =1344

Answer:

n = 3

Step-by-step explanation:

1) Divide both sides by 3.5

n = 10.5/3.5

2) Simplify 10.5/3.5 to 3

n = 3

"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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The amount of sandwich they eat altogether is 2/3

A fraction can be defined as the part of a whole number, a whole number, a whole element.

The different types of fractions are listed as;

From the information given, we have that;

Angie ate 1 / 3 of the sandwich

Kim ate another 1 / 3 of the sandwich

To determine the total amount, we have;

1/3 + 1/3

add the values

1 + 1/3

add the values, we get;

2/3

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The complete question:

Angie and Kim are sharing a large sub sandwich. Angie ate 1 / 3 of the sandwich, and Kim ate another 1 / 3 of the sandwich. Please work out in detail.

Answer:

\(\frac{3}{11}\), 28, \(\frac{4}{11}\)

Step-by-step explanation:

For the first one, you would subtract \(\frac{5}{11}\) from \(\frac{8}{11}\), giving you \(\frac{3}{11}\).

For the second one, you would subtract 22 from 50, giving you 28.

For the third one, you would subtract \(\frac{4}{11}\) from \(\frac{8}{11}\), giving you \(\frac{4}{11}\).

Hope I helped

In Indian numerical system (or number system) is a written system that is adapted for representing numbers within India.

Given:

27,974

\(\to \bold{20,000 +7,000+ 900+ 70 +4=27,974} \\\\\to \bold{27\ thousands + 97\ tens + 4\ ones =27,974}\\\\OR\\\\\to \bold{27\ thousands + 9\ hundred + 74 =27,974}\\\\\)

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Answer:

66

Step-by-step explanation:

(z-33)/z = 1/2

2z-66=z

z=66

Answer:

36

Step-by-step explanation:

15 divided by 5 would = 3

3 is the cost of 1 cupcake

3 x 12 is 36

Answer:

36

Step-by-step explanation:

The pattern is times 3 so 12 times 3 is 36

Answer:

1/20

Step-by-step explanation:

1/10x5/10=5/100=1/20

The simplified expression is \(-4x^2 + 3x + 1\), which is a quadratic polynomial. Option D.

To simplify the expression \((8x^2 + 3x) - (12x^2 - 1)\), we can distribute the negative sign to each term within the parentheses:

\(8x^2 + 3x - 12x^2 + 1\)

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

\((8x^2 - 12x^2) + 3x + 1\)

Simplifying further, we have:

\(-4x^2 + 3x + 1\)

The resulting polynomial \(-4x^2 + 3x + 1\) is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is\(-4x^2.\)Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression \((8x^2 + 3x) - (12x^2 - 1)\) simplifies to \(-4x^2 + 3x + 1\) , which is a quadratic polynomial. So Option D is correct

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Note the complete question is

Answer:

2

Step-by-step explanation:

1/2 divided by 1/4 rewritten is 1/2 times 4/1 equels 4/2. In its simplest form 2.

1/2 divided by 1/4 in the simplest form is 2.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given that the expression 1/2 divided by 1/4.

simplifying,

1/2 divided by 1/4  = 1/2 ÷ 1/4

Rearranging into the multiplication form,

1/2 divided by 1/4 = 4/2

1/2 divided by 1/4 = 2

Therefore, the simplest form of 1/2 divided by 1/4 is 2.

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

(x - 3)² + (y - 2)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (3, 2 ) and r = 5 , then

(x - 3)² + (y - 2)² = 5² , that is

(x - 3)² + (y - 2)² = 25 ← equation of circle

Answer:

-11/5

Step-by-step explanation:

In order to solve it u should open the mixed fraction ,i.e,

11/7÷-15/21

=11/7×-21/15

Cutting,

ans=-11/5

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Answer:

Fraction: -11/5

Decimal form: -2.2

Mixed number form: -2 1/5

Step-by-step explanation:

a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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