A 50 inch smart tv is on sale with a 25% discount. The original price is $429. What is the sale price?

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Answer:

a is the answer as it has 2 constant terms in 3 variables

Step-by-step explanation:

constant means a no. (it doesnt changes)

ex. 2 , 7 etc

variable means a term (generally a letter) which changes, its value will differ.

in the equation you have given both have only 2 variables

have you posted all the options?

GOOD LUCK FOR THE FUTURE! :)

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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The length of CD is 26.0 cm.

The sine rule is for solving triangles which are not right-angled in which two sides and the included angle are given.

In ΔABC:

sin 35° = AB/BD

sin 35° = 12/BD

BD = 12/sin 35°

BD = 20.92 cm

Using sine rule:

CD/sin B = BD/ sin C

CD/sin 102° = 20.92/ sin 52°

CD = (20.92 * sin 102°) / sin 52°

CD = 26.0 cm

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Complete Question

Check attached image

Answer:

(x-1)(4x-3)(x+3)

Step-by-step explanation:

The factor of the polynomial 4x³ + 5x² – 18x + 9 will be (4x – 3), (x + 3), and (x – 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ 4x³ + 5x² – 18x + 9

Then the factor of the polynomial will be

⇒ 4x³ – 3x² + 8x² – 6x – 12x + 9

⇒ x²(4x – 3) + 2x(4x² – 3) – 3(4x – 3)

⇒ (4x – 3)(x² + 2x– 3)

⇒ (4x – 3)(x² + 3x – x – 3)

⇒ (4x – 3)(x + 3)(x – 1)

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Answer:

m = -21.

Step-by-step explanation:

To solve this equation, we can use the distributive property to expand the left side and the right side of the equation:

19(2m - 16) = 13(2m + 4)

38m - 304 = 26m + 52

Then we can combine like terms on both sides of the equation to obtain:

38m - 26m = 52 - 304

12m = -252

Finally, we can divide both sides of the equation by 12 to find the value of m:

12m / 12 = -252 / 12

m = -21

Therefore, the value of m that satisfies the equation is m = -21.

\(4.371cm^{2}\)  and \(25.85cm^{2}\)  are the dimension of the cylindrical container  that will minimize the cost of the container .

As we know  ,The volume of a cylinder is :355=πr²h  ,where r is the radius of the base and  h is the height. hence ,

\(h=\)\(\frac{355}{\pi r^{2} }\) , so radius and area can be substituted , 2A=2πr² ,  the cost of  

0. 02 cents per cm² and a rectangular component  of area  A=2πrh , with cost of 0. 03 cents per cm², hence the cost function  of a cylinder is:

C=0.02(2πr²)+0.03(2πrh)

C=0.04(πr²)+0.06(πrh)

C=0.04(πr²)+0.06(πr(350/πr²)) (on substituting h)

C=0.04(πr²)+(21/r), ( on differentiating both sides  )

C'=0.08(πr)-(21/r²)= 0,

r= 3√525/2π =4.371

355/π(3√(525/2π))  = 355/π(3√(83.55))  =350/π( 4.371) =25.85

the value of h is 25.58 \(cm^{2}\)

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Answer:

(a) a = 22 or 2

(b) The equations of AD are

y = x/2 + 7

or

y = x/2 + 17

(c) The equation of CD is y = -2·x - 3

(d) The coordinate of the point D is either (-8, 13) or (-4, 5)

(e) the possible areas are;

250 square units or 270 square units

Step-by-step explanation:

With only the details of the trapezium, without the drawing, we have as follows;

(a) The given points are;

A(a, 18), B(12, -2), and C(2, -7)

The length of BC is given from the formula for finding the length, l, of a line with the coordinates of the end points as follows;

\(l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

\(l_{BC} = \sqrt{\left ((-7)-(-2) \right )^{2}+\left ((2)-(12) \right )^{2}} = \sqrt{\left ((-5) \right )^{2}+\left (-(10) \right )^{2}} = 5\cdot \sqrt{5}\)

∴ From \(l_{AB} = l_{BC}\), we have;

\(l_{AB}\) = 2 × 5·√5 = 10·√5

Which gives;

\(l_{AB} = \sqrt{\left ((18)-(-2) \right )^{2}+\left (a-12 \right )^{2}} = \sqrt{\left 20 \right ^{2}+\left (a-12 \right )^{2}}= 10 \cdot \sqrt{5}\)

20² + (a - 12)² = 500

(a - 12)² = 500 - 20² = 500 - 400 = 100

(a - 12)² = 100

a - 12 = ±√100 = ±10

a = 10 + 12 or -10 + 12

a = 22 or 2

(b) The equation of BC is given as follows;

The slope, m, of BC = (-7 -(-2)/(2 - 12) = -5/-10 = 1/2

The equation of BC is therefore;

y - (-7) = 1/2×(x - 2)

y + 7 = x/2 - 1

y = x/2 - 1 - 7 = x/2 - 8

y = x/2 - 8

Therefore, the slope of AD = m = 1/2

The equation of AD can be

y - 18 = 1/2×(x - 22)

y = x/2 -11 + 18 = x/2 + 7

y = x/2 + 7

or

y - 18 = 1/2×(x - 2)

y = x/2 -1+ 18 = x/2 + 17

y = x/2 + 17

(c) The equation of CD is given as follows;

CD is perpendicular to BC, therefore, the slope of CD = -1/m = -2

The equation of CD is therefore;

y - (-7) = -2×(x - 2)

y = -2·x + 4 - 7 = -2·x - 3

y = -2·x - 3

(d) The coordinate of the point D is found as follows;

At point D,

At

x/2 + 17=-2·x - 3

2.5·x = -20

x = -8

y = -8/2 + 17 = 13

or

x/2 + 7 =-2·x - 3

2.5·x = -10

x = -4

y = -4/2 + 7 = 5

The possible coordinates of the point D are (-8, 13) or (-4, 5)

(e) The area of the trapezium is found as follows;

The vertices points are;

(2, 18) or (22, 18), (12, -2), (2, -7) and (-8, 13) or (-4, 5)

The formula for the area of a trapezium = (a + b)/2×h

Length of a = \(l_{BC}\) =  5·√5

h = \(l_{CD} = \sqrt{\left ((13)-(-7) \right )^{2}+\left ((-8)-2 \right )^{2}} = \sqrt{\left 20 \right ^{2}+10^{2}}= 10 \cdot \sqrt{5}\)

or

\(l_{CD} = \sqrt{\left ((5)-(-7) \right )^{2}+\left ((-4)-2 \right )^{2}} = \sqrt{\left 12 \right ^{2}+6^{2}}= 6 \cdot \sqrt{5}\)

b = \(l_{AD} = \sqrt{\left (13-18 \right )^{2}+\left ((-8)-2 \right )^{2}} = \sqrt{\left (-5 \right )^{2}+(-10)^{2}}= 5 \cdot \sqrt{5}\)

\(l_{AD} = \sqrt{\left (5-18 \right )^{2}+\left ((-4)-22 \right )^{2}} = \sqrt{\left (-13 \right )^{2}+(-26)^{2}}= 13 \cdot \sqrt{5}\)

Therefore, the possible areas are;

(5×√5 + 5×√5)/2 × 10×√5 = 250 square units

(5×√5 + 13×√5)/2 × 6×√5 = 270 square units

The value of 'a' is 22 or 2, the equation of AD is (y = 0.5x + 17) or (y = 0.5x + 7) and the point D is (-8,13) or (-4,5) and this can be determine by using the point slope form.

Given :

a) To determine the value of 'a' use the relation (AB = 2 BC).

\(\sqrt{(12-a)^2+(-2-18)^2}=2\times \sqrt{(2-12)^2+ (-7+2)^2}\)

\(\sqrt{(12-a)^2+400}=2\times \sqrt{125}\)

Squaring both sides in the above expression.

\((12-a)^2+400=4\times 125\)

\(144+a^2-24a=100\)

\(a^2-24a+44=0\)

\(a^2-22a-2a+44=0\)

\(a(a-22)-2(a-22) = 0\)

a = 2 or 22

b) The equation of BC is given by:

\(\dfrac{y+2}{x-12}=\dfrac{-7+2}{2-12}\)

\(2(y+2)=(x-12)\)

2y + 4 = x - 12

2y - x + 16 = 0

y = 0.5x - 8

Given that AD is parallel to BC so, the slope of 0.5.

First, take a = 2. The equation of line AD is given by:

\(y-18 =0.5(x-2)\)

Now, take a = 22. The equation of line AD is given by:

\(y-18 =0.5(x-22)\)

c) The line CD is perpendicular to line BC. So, the slope of line CD is -2. The equation of the line CD is given by:

y - (-7) = -2(x - 2)

y + 7 = -2x + 4

y + 2x + 3 = 0

d) The point D is given by:

0.5x + 17 = -2x - 3

2.5x = -20

x = -8

y = -4 + 17 = 13

or

0.5x + 7 = -2x - 3

x = -4

Now, y = - 2 + 7 = 5

e) Area of the trapezium is given by:

\(\rm A = L_{CD} \times L_{AD}\)

So, the possible area of the trapezium is:

\(\dfrac{(5\times \sqrt{5} +5\times \sqrt{5} )}{2}\times 10 \times \sqrt{5} = 250\)

\(\dfrac{(5\times \sqrt{5} +13\times \sqrt{5} )}{2}\times 6 \times \sqrt{5} = 270\)

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's evaluate ~

\(\qquad \tt \dashrightarrow \:(6 \times 1000) + (1 \times 10) + (8 \times \frac{1}{1} ) + (9 \times \frac{1}{10} ) + \frac{4}{100} \)

\(\qquad \tt \dashrightarrow \:6000 + 10 + 8 + \frac{9}{10} + \frac{4}{100} \)

\(\qquad \tt \dashrightarrow \: \dfrac{600000 + 1000 + 800 + 90 + 4}{100} \)

\(\qquad \tt \dashrightarrow \: \dfrac{601894}{100} \)

or

\(\qquad \tt \dashrightarrow \:{6018.94}{} \)

The Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding.

a. The Effective Annual Rate (EAR) for 12% compounded quarterly is 12.55%. To calculate this, we use the formula EAR = (1 + r/n)^n - 1, where r is the nominal annual interest rate and n is the number of times interest is compounded in a year. Plugging in the values, we get EAR = (1 + 0.12/4)^4 - 1 = 0.1255 or 12.55%.

b. The Effective Annual Rate (EAR) for 7% compounded monthly is 7.23%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.07/12)^12 - 1 = 0.0723 or 7.23%.

c. The Effective Annual Rate (EAR) for 16% compounded daily is 17.47%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.16/365)^365 - 1 = 0.1747 or 17.47%.

d. The Effective Annual Rate (EAR) for 12% with continuous compounding is 12.75%. To calculate this, we use the formula EAR = e^r - 1, where e is the mathematical constant approximately equal to 2.71828 and r is the nominal annual interest rate. Plugging in the values, we get EAR = e^(0.12) - 1 = 0.1275 or 12.75%.

In summary, we can say that the Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding. The EAR takes into account the effect of compounding on the nominal interest rate, providing a more accurate representation of the true cost of borrowing or the true return on an investment.

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To determine the minimum diameter of the rod, we can use the formula for bending stress:

σ = (M * c) / (I * y)

Where:

σ is the bending stress

M is the bending moment

c is the distance from the neutral axis to the outermost fiber

I is the moment of inertia of the cross-section

y is the perpendicular distance from the neutral axis to the point where the stress is being calculated

Given:

M = -1000 lbf.in

σ = 32 kpsi = 32,000 psi

Strength = 25 kpsi

Design factor = 2.5

First, we need to convert the bending moment to pound-force feet (lbf.ft):

M = -1000 lbf.in = -83.33 lbf.ft (1 lbf.in = 0.0833 lbf.ft)

Next, we can rearrange the bending stress formula to solve for the moment of inertia (I):

I = (M * c) / (σ * y)

Since we are looking for the minimum diameter, we want to minimize the moment of inertia. This occurs when the rod is a solid cylinder with its maximum diameter.

The moment of inertia of a solid circular rod is given by the formula:

I = (π * d^4) / 64

Substituting the formulas and given values, we can solve for the minimum diameter (d):

(π * d^4) / 64 = (M * c) / (σ * y)

d^4 = (64 * M * c) / (π * σ * y)

d = ∛((64 * M * c) / (π * σ * y))^0.25

Once we have the minimum diameter (d), we can select a preferred fractional diameter from the table provided and calculate the resulting factor of safety using the formula:

Factor of Safety = (Strength * Design Factor) / σ

Please provide the values of c, y, and the preferred fractional diameter from the table so that I can help you with the calculations.

The minimum diameter of the rod is approximately 1.37 inches.A preferred fractional diameter that corresponds to a factor of safety greater than or equal to 0.78125, ensuring a safe design.

a) To determine the minimum diameter of the rod, we can use the formula for bending stress:

σ = M / (0.25 * π * (d^3))

Rearranging the formula, we have:

d^3 = M / (0.25 * π * σ)

Substituting the given values, we get:

d^3 = 1000 / (0.25 * π * 32)

Solving for d, we find:

d ≈ 1.37 inches

Therefore, the minimum diameter of the rod is approximately 1.37 inches.

b) To select a preferred fractional diameter and calculate the resulting factor of safety, we need to compare the calculated stress with the material strength and design factor.

Given the stress σ = 32 kpsi and a material strength of 25 kpsi, we can calculate the factor of safety:

Factor of Safety = (Material Strength) / (Design Stress)

Factor of Safety = 25 / 32

Factor of Safety ≈ 0.78125

Referring to the provided table, we can choose a preferred fractional diameter that corresponds to a factor of safety greater than or equal to 0.78125, ensuring a safe design.

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The required f(x) values are  5, 1 , -1 , -3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

f(x)= -2x+1

Substitute the values for x and find the value of f(x)

For x= -2:

f(x)= -2(-2)+1

    = 5

For x= 0:

f(x)= -2(0)+1

    = 1

For x= 1:

f(x)= -2(1)+1

    = -1

For x= -2:

f(x)= -2(2)+1

    = -3

The required f(x) values are  5, 1 , -1 , -3

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Answer:

what is that ............

Answer:

D.  296 square inches

Step-by-step explanation:

The surface area of a prism is the total area of all its faces.

A triangular prism has three rectangular faces and two triangular faces.

As all 3 sides of the triangle face of this prism are equal, each of the 3 rectangular faces are also equal in area.

Formulae

From inspection of the diagram:

⇒ Area of a triangle = 1/2 x 8 x 7 = 28 in²

⇒ Area of a rectangle = 8 x 10 = 80 in²

Total surface area

Total surface area = 3 rectangle areas + 2 triangle areas

                              = (3 x 80) + (2 x 28)

                              = 296 in²

Answer:

296

Step-by-step explanation:

have a great day

The measure of angle R is 106.5 degrees approximately when the

sides of the triangle are given.

If ABC is a triangle, then as per the statement of the Law of Cosines, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.

Here PQR is a triangle, then as per the statement of cosine law,

we will have:  p2 = q2 + r2 – 2pqcos R,

where p, q  and r are the sides of triangle and R is the angle between sides q and p.

therefore, \(28^{2} = 17^{2} +15^{2}\) - 2(28)(17)cos R

              cos R = -270/952

                        = -0.284

                    R = cos-1(-0.284)

              therefore, R = 106.499 = 106.5 approximately.

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Explanation:

They start on the 20 yard line. After the first play, they gain 10 yards and move to the 20+10 = 30 yard line.

After the second play, they must have gained 20 yards because 30+20 = 50.

Or you can think of it like 50-30 = 20, which shows the distance from the 30 yard line to the 50 yard line is 20 yards.

All of this assumes that the Cowboys started on their side of the field.

Answer:

here is the answer, I had sent a photo. Do you see it.

Answer:

2240

Step-by-step explanation:

braniest pls

there are 2,240 women at the college.

To find the number of women at the college, we can use the ratio of men to women given and the known number of men.

The ratio of men to women is 5 to 4, which can be expressed as 5/4.

If we know that there are 2,800 men, we can set up a proportion:

5/4 = 2,800/x

To solve for x, the number of women, we cross-multiply:

5x = 4 * 2,800

5x = 11,200

Dividing both sides by 5:

x = 11,200 / 5

x = 2,240

Therefore, there are 2,240 women at the college.

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Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

Answer:

Below in bold.

Step-by-step explanation:

3n + 4:

The common difference = 3,

First term = 3(1) + 4 = 7

First 4 terms

= 7, 10, 13, 16

10th term = 3(10) + 4 = 34.

4n - 5:

The common difference = 4,

First term = 4(1) - 5 = -1

First 4 terms

= -1, 3, 7, 11

10th term = 4(10) - 5 = 35.

Answer:

(0,4)

it was correct

You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.

Janice's monthly payment for her 5-year, 4% APR car loan would be $626.38.

To calculate Janice's monthly payment, we first need to use the formula for calculating loan payments:

Loan Payment = Loan Amount / Discount Factor

The discount factor can be calculated using the following formula:

Discount Factor = [(1 + r)ⁿ] - 1 / [r(1 + r)ⁿ]

Where r is the monthly interest rate (4% divided by 12 months = 0.00333) and n is the total number of payments (5 years x 12 months = 60).

Plugging in the values, we get:

Discount Factor = [(1 + 0.00333)⁶⁰] - 1 / [0.00333(1 + 0.00333)⁶⁰] = 55.8389

Now, we can calculate Janice's monthly payment:

Loan Payment = $35,000 / 55.8389 = $626.38

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Profit Maximizing Quantity (Q) is the output level at which a company generates the highest possible profit while maintaining its price and marginal costs. The formula for calculating the Profit Maximizing Quantity is MR = MC.In the first demand and cost function, the demand function is:

Q = 31.175-25P, where P is the price and Q is the quantity sold.

C(Q) = -689Q + 5075. Here, C(Q) is the cost function.We know that the marginal cost of the product (MC) equals the derivative of the cost function;

MC = C’(Q) = -689.

We also know that, since demand is a function of price and price is a function of quantity, we can use the chain rule to get the inverse demand function (P = P(Q)):

dP/dQ = dP/dQ * dQ/dP => 1/(-25) = dP/dQ => -0.04 = dP/dQ

We can use this relationship to obtain MR (marginal revenue) by multiplying both sides by P:

MR = P * (-0.04) = -0.04P.

The profit-maximizing quantity is determined by setting MR equal to MC:

MR = MC => -0.04P = -689 => P = 17225.

The inverse demand function (P = P(Q)) can be used to determine the quantity sold at the profit-maximizing price:17225 = 31.175-25Q => 25Q = -17193.825 => Q = -687.753

This solution is impossible because the quantity must be positive.

As a result, there is no profit-maximizing quantity in this scenario.In the second demand and cost function, the demand function is:

Q = -2,314-89P,

where P is the price and Q is the quantity sold.C(Q) = 12Q + 13.54. Here, C(Q) is the cost function.

The marginal cost of the product (MC) equals the derivative of the cost function;

MC = C’(Q) = 12.We also know that, since demand is a function of price and price is a function of quantity, we can use the chain rule to get the inverse demand function (P = P(Q)):

dP/dQ = dP/dQ * dQ/dP => 1/(-89) = dP/dQ => -0.01123595 = dP/dQ

We can use this relationship to obtain MR (marginal revenue) by multiplying both sides by P:

MR = P * (-0.01123595) = -0.01123595P.

The profit-maximizing quantity is determined by setting MR equal to MC:

MR = MC => -0.01123595P = 12 => P = -1066.13.

The inverse demand function (P = P(Q)) can be used to determine the quantity sold at the profit-maximizing price:-1066.13 = -2,314-89Q => 89Q = 1248.13 => Q = 14.

The profit-maximizing quantity (Q) is 14.

In the graph, we can see that the profit maximizing output is at 168.

To calculate the profit at the profit maximizing output, we need to find the point of intersection between the MR and MC curves and then multiply the quantity by the difference between the price (P) and average total cost (ATC) to get the profit.

The point of intersection in this case is approximately (168, 21).The price is 21 and the ATC is 10, therefore the profit is (21-10) * 168 = 1848. Answer: 1848

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The p-value = 0.078, Since p-value = 0.0708 < 0.10  significance level, we reject H0.

i) Claim: The population proportion is now greater than 35%

ii) Null hypothesis: H0: p = 0.35

iii) Alternative hypothesis: Ha: p > 0.35

iv) Test statistic:

\(z = \frac{p-p}{\sqrt{\frac{p*(1-p)}{n} } }\)

Where

\(p = \frac{x}{n}= \frac{42}{100} = 0.42\)

Thus

\(z = \frac{0.42-0.35}{\sqrt{\frac{0.35*0.65)}{100} } }\\\\z = \frac{0.07}{\sqrt{\frac{0.35*0.65)}{100} } }\\\\z = \frac{0.07}{\sqrt{0.002275} } }\\\\z = \frac{0.07}{0.047697}\)

Z = 1.47

v) p-value:

p-value = P( Z > z test statistic value)

p-value = P( Z > 1.47 )

p-value = 1 -  P( Z < 1.47 )

Look in z table for  z = 1.4 and 0.07 and find area.

From z table , we get:

P( Z < 1.47)=  0.9292

Thus

p-value = 1 -  P( Z < 1.47 )

p-value = 1 - 0.9292

p-value =  0.0708

Thus reject H0 if p-value < 0.10 significance level, otherwise we fail to reject H0.

vi) Decision:

Since p-value = 0.0708 < 0.10  significance level, we reject H0.

vii) Interpretation:

Since we have rejected null hypothesis H0 at .10 significance level, there is sufficient evidence to support the claim that The population proportion is now greater than 35% that is: the population proportion of students at UCLA who have traveled abroad has increased after the implementation of the study abroad program.

Hence the answer is the p-value = 0.078, Since p-value = 0.0708 < 0.10  significance level, we reject H0.

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To test if there is a difference between the means of the two populations, we can perform a two-sample t-test. The null hypothesis is that there is no difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

Let's assume that the researcher has collected the following data:

Sample of families with no children: n1 = 30, sample mean = 4.5 hours per week, sample standard deviation = 1.2 hours per week.

Sample of families with children: n2 = 40, sample mean = 3.8 hours per week, sample standard deviation = 1.5 hours per week.

Using the critical value method, we need to calculate the t-statistic and compare it to the critical value from the t-distribution table with n1+n2-2 degrees of freedom and a significance level of α = 0.05.

The formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the numbers, we get:

t = (4.5 - 3.8) / sqrt((1.2^2/30) + (1.5^2/40)) = 2.08

The degrees of freedom for the t-distribution is df = n1 + n2 - 2 = 68.

Using a t-distribution table, we find the critical value for a two-tailed test with α = 0.05 and df = 68 is ±1.997.

Since our calculated t-statistic of 2.08 is greater than the critical value of 1.997, we can reject the null hypothesis and conclude that there is a statistically significant difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

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The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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The value of ∠BAC is 50°. Hence, the correct option is 50º.Given, AD is tangent to circle B at point C. ∠ABC = 40°.We need to find the value of ∠BAC.Therefore, let's solve this problem below:As AD is tangent to circle B at point C, it forms a right angle with the radius of circle B at C.

∴ ∠ACB = 90°Also, ∠ABC is an external angle to triangle ABC. Therefore,∠ABC = ∠ACB + ∠BAC = 90° + ∠BACNow, putting the value of ∠ABC from the given information, we get,40° = 90° + ∠BAC40° - 90° = ∠BAC-50° = ∠BAC

Therefore, the value of ∠BAC is 50°. Hence, the correct option is 50º.

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Answer:

2,400

Step-by-step explanation:

The email with an open rate of 9.6% was opened by 2400 people.

The open rate of email campaigns = 9.6%

number of emails = 25000

The percentage is the value per hundred.

For example, A students got 800 marks out of 1000 marks. So, his percentage will be 800/1000 *100 = 80%

So, 9.6% of 25000 = 9.6*25000/100

9.6% of 25000 = 9.6*250

9.6% of 25000 = 2400

So, the email was opened by 2400 people.

Therefore, the email was opened by 2400 people.

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