Evaluate the algebraic expression for the given values of the variables

The list price of each camera is approximately $26.59.

Let's assume the list price of each camera is represented by 'x'.

According to the given information, the merchant sold a certain number of cameras at the list price and received a total of $432. This can be expressed as:

Number of cameras * List price = Total revenue

x * Number of cameras = $432

Now, if the merchant had three more cameras and sold each one for $12 less, the new selling price would be (x - $12). The total revenue would still be $432. This can be expressed as:

(New number of cameras) * (New selling price) = Total revenue

(x + 3) * (x - $12) = $432

Expanding the equation:

x^2 - $12x + 3x - $36 = $432

x^2 - 9x - $468 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring this equation may not yield integer solutions, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -9, and c = -468. Plugging these values into the quadratic formula:

x = (-(-9) ± √((-9)^2 - 4 * 1 * (-468))) / (2 * 1)

x = (9 ± √(81 + 1872)) / 2

x = (9 ± √(1953)) / 2

Calculating the square root of 1953 gives us approximately 44.17. Therefore, the two possible values for x are:

x1 = (9 + 44.17) / 2 ≈ 26.59

x2 = (9 - 44.17) / 2 ≈ -17.59

Since the price of a camera cannot be negative, we discard x2. Therefore, the list price of each camera is approximately $26.59.

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The system has exactly one solution. The solution is (13, 8)

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

Country A: -x + 20y = 147

Country B: -x + 10y = 67

Country C: y = 8

So, we have

-x + 20y = 147

-x + 10y = 67

y = 8

Substitute 8 for y in the first and second equations

So, we have

-x + 20 * 8 = 147

-x + 10 * 8 = 67

Evaluate the products

-x + 160 = 147

-x + 80 = 67

So, we have

x = 160 - 147

x = 80 - 67

Evaluate

x = 13

x = 13

Hence, the solution to the system of equations is (13, 8)

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The correct expression to calculate the area of a triangle with a base of 21 inches and height of 12 inches is (21 × 12) ÷ 2.

The subject of your question is Mathematics, specifically dealing with the topic of how to calculate the area of a triangle. The formula to calculate the area of a triangle is 1/2 multiplied by the base multiplied by the height. So, in your question where the base of the triangle is 21 inches and the height is 12 inches, the correct choice would be D. (21 × 12) ÷ 2 which applies the formula correctly.

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The correct option is A. [13(cos 22.6 - isin 22.6)] in which the modulus is 13 and the argument is 22.6 degrees.

Given the complex number z = 12 + 5i. We have to express this complex number in the polar form which is\[z=r\cos\theta + i\sin\theta\]where r is the modulus and θ is the argument of the complex number.

The modulus of the complex number is given by,|z|=√(12²+5²)=√(144+25)=√169=13

Therefore, the modulus of the complex number is 13.

Now, we need to find the argument of the complex number, which is given byθ=tan⁻¹(b/a)Where a and b are the real and imaginary parts of the complex number z.θ=tan⁻¹(5/12)So, θ=22.6 degrees. (approximate value)

Thus, the complex number z = 12 + 5i can be expressed as\[z=13\cos(22.6^{\circ}) + i\sin(22.6^{\circ})

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By applying the algebraic identity, the expression (24)³ - (13)³ - (11)³ can be simplified as (11)(1057) - (11)³ = 10396, without actually calculating the cubes.

The expression (24)³ - (13)³ - (11)³ can be evaluated without calculating the cubes by applying the concept of algebraic identities.

By using the identity (a³ - b³) = (a - b)(a² + ab + b²), we can rewrite the expression as (24 - 13)(24² + 24*13 + 13²) - (11)³.

Simplifying further, we have (11)(576 + 312 + 169) - (11)³.

Combining like terms, the expression evaluates to (11)(1057) - (11)³.

Finally, we can simplify to obtain the result of 11 multiplied by 1057 minus 11 cubed, without actually calculating the cubes. The simplified expression (24)³ - (13)³ - (11)³ evaluates to 10396.

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11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.

12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.

In Mathematics and Geometry, a perpendicular bisector can be used for bisecting or dividing a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.

Question 11.

By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB:

AC ≅ BC

CD ≅ CD

AE ⊥ EC

Question 12.

By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.

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Answer:

Region A: 20,178 people/521 km²

= 38.7 people/km²

Region B: 1,200 people/451 km²

= 2.7 people/km²

Region C: 13,475 people/395 km²

= 34.1 people/km²

Region D: 6,980 people/426 km²

= 16.4 people/km²

The regions, in order from the most densely populated to the least densely populated: A, C, D, B

The midpoint of the line segment joining the pair of points (8, -8) and (-5, -1) is (1.5, -4.5).

To find the midpoint, we need to take the average of the x-coordinates and the average of the y-coordinates of the two given points.

For the x-coordinate: (8 + (-5))/2 = 3/2 = 1.5

For the y-coordinate: (-8 + (-1))/2 = -9/2 = -4.5

Thus, the midpoint of the line segment is (1.5, -4.5).

In more detail, the midpoint formula is derived by averaging the x-coordinates and y-coordinates separately. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint (xm, ym) is given by:

xm = (x1 + x2)/2

ym = (y1 + y2)/2

In this case, the x-coordinates are 8 and -5, and their average is (8 + (-5))/2 = 1.5. The y-coordinates are -8 and -1, and their average is (-8 + (-1))/2 = -9/2 = -4.5.  

Therefore, the midpoint of the line segment joining the two given points is (1.5, -4.5).

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The statistical questions for this problem are given as follows:

A question is classified as statistical if it can receive answers of data that vary, that is, questions that do not have an exact answer.

When the answer is exact, it must be composed by a set of data, such as the number of students that like football in each school, the number will vary for each school.

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According to slope intersept form : y = mx+b

m is slope and b is y intersept

so y = -6x+5

slope(m) = -6

y intersept = 5

HOPE IT HELPS

PLEASE GIVE BRAINLIEST

Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

Answer:

? = 157°

Step-by-step explanation:

the measure of the secant- secant angle KLM is half the difference of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (CJ - KM) = ∠ KLM , that is

[tex]\frac{1}{2}[/tex] (? - 53) = 52° ( multiply both sides by 2 to clear the fraction )

? - 53° = 104° ( add 53° to both sides )

? = 157°

Answer:

F(5)= -1

if 5 is the value on the x axis it corresponds to -1 on the y axis

In order to achieve a profit of $123,525, the Vilas County News would require a subscriber base of 6,355,500 individuals.

Let's break down the problem step by step to find the number of subscribers needed to bring a total profit of $123,525.

First, we know that the Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. This means that the current profit from the 3,000 subscribers is $20 x 3,000 = $60,000.

Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. This means that for every additional subscriber, the profit increases by $0.01. Therefore, we need to find how many additional subscribers are required to reach a total profit of $123,525 - $60,000 = $63,525.

To find the number of additional subscribers needed, we divide the additional profit required by the increase in profit per subscriber: $63,525 / $0.01 = 6,352,500.

However, we need to remember that this number represents the total number of additional subscribers needed, not the final total number of subscribers. To find the final total number of subscribers, we add the additional subscribers to the current number of subscribers: 6,352,500 + 3,000 = 6,355,500.

Therefore, to bring a total profit of $123,525, the Vilas County News would need a total of 6,355,500 subscribers.

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Answer:

D. 45 square feet

Step-by-step explanation:

To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular lateral faces.

First, let's find the area of the base (square).

[tex]\boxed{\begin{minipage}{7 cm}Base area = side length $\times$ side length\\ \\Base area = 3 $\times$ 3 \\ \\Base area = 9 square feet\end{minipage}}[/tex]

Now, let's find the area of the triangular lateral faces.

As stated in the problem, the slant height of the triangle is 6 feet. We can find the area of one triangular lateral face:

[tex]\text{Triangle area = $\frac{1}{2}$ $\times$ base $\times$ height}\\\\\text{Triangle area = $\frac{1}{2}$ $\times$ 3 $\times$ 6} \\\\\text{Triangle area = 9 square feet}[/tex]

Since there are four triangular lateral faces, we need to multiply this area by 4:

[tex]\text{Total lateral area = 4 $\times$ 9}\\\\\text{Total lateral area = 36 square feet}[/tex]

Finally, we add the base area and the total lateral area to find the total surface area of the pyramid:

[tex]\text{Total surface area = base area + total lateral area}\\\\\text{Total surface area = 9 + 36}\\\\\text{Total surfacel area = 45 square feet}[/tex]

So, the area of the square pyramid is 45 square feet. Which is option D.

________________________________________________________

Answer:

  D.  45 square feet

Step-by-step explanation:

You want the surface area of a square base pyramid with a side length of 3 feet and a slant height of 6 feet.

The area of a triangular face is given by ...

  A = 1/2bh . . . . . base b and height h

The area of the square base is given by ...

  A = s²

The total surface area of the pyramid is the area of the base plus the areas of the 4 triangular faces:

  total area = s² +4(1/2bh) . . . . where b = s

This can be simplified to ...

  total area = s(s +2h) . . . . . area of a square pyramid with slant height h

For the pyramid with a square base 3 ft on a side, and a slant height of 6 ft, the total area is ...

  total area = (3 ft)(3 ft + 2·6 ft) = (3 ft)(15 ft) = 45 ft²

The area of the pyramid is 45 square feet.

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Answer:

Any equation that has the power of x at 1

Step-by-step explanation:

Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work

Answer:

- 15pr

Step-by-step explanation:

- 5p(3r) ← means multiply 3r by - 5p

= - 5p × 3r

= - 5 × 3 × p × r

= - 15 × pr

= - 15pr

Answer:

Volume : 300

Surface Area : 280

Step-by-step explanation:

Volume : 6*5*10

Surface Area : 50+50+30+30+60+60

The probability of taking the smallest ball at least once during 4 tries can be calculated as 1 minus the probability of not taking the smallest ball in any of the 4 tries. Since each try is independent and the probability of not taking the smallest ball in a single try is 9/10, the probability of not taking it in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561. Therefore, the probability of taking the smallest ball at least once during 4 tries is 1 - 0.6561 = 0.3439, or approximately 34.39%.

To find the probability of not taking the smallest ball in any of the 4 tries, we need to calculate the probability of not selecting the smallest ball in each try and then multiply them together.

In each try, there are 9 balls remaining that are not the smallest ball, out of a total of 10 balls. Therefore, the probability of not taking the smallest ball in a single try is 9/10.

Since the tries are independent events, we can multiply the probabilities together to find the probability of not taking the smallest ball in all 4 tries.

After calculating this probability, we subtract it from 1 to obtain the probability of taking the smallest ball at least once during the 4 tries.

In this case, the probability of not taking the smallest ball in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561.

Finally, subtracting this value from 1 gives us the probability of taking the smallest ball at least once, which is 1 - 0.6561 = 0.3439, or approximately 34.39%.

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Answer:

24310

Step-by-step explanation:

17 choose 8= 17 choose 9

17 choose 8= 17*16*15*14*13*12*11*10/8!= 24310

The y-intercept, b, can be calculated as:

b = (Σy - mΣx) / n

To find the regression line associated with the set of points (4, 6), (6, 10), (10, 14), and (12, 2), we can use the least squares method. The regression line represents the best-fit line that minimizes the sum of the squared differences between the observed y-values and the predicted y-values on the line.

The equation for the regression line, y(x), can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

Using the given points, we can calculate the slope, m, and the y-intercept, b, to obtain the equation of the regression line.

The slope, m, is calculated as:

m = (nΣxy - ΣxΣy) / (nΣ[tex]x^2[/tex] - (Σ[tex]x)^2[/tex])

where n is the number of points, Σxy is the sum of the product of x and y values, Σx is the sum of the x-values, and Σy is the sum of the y-values.

Similarly, the y-intercept, b, can be calculated as:

b = (Σy - mΣx) / n

By substituting the given values into the formulas and performing the calculations, the equation for the regression line can be obtained.

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To find the volume of the given cylinder, we need to use the formula of volume of a cylinder which is given by V = πr²h, where V is the volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder. So, the volume is 1078.1 cubic units.

Given, Length = 14 units, Height = 11 units. Now, we know that the formula for the volume of a cylinder is given as; V = πr²h.

Here, the radius of the cylinder is half the length of the cylinder, which is; Radius = Length/2

Radius = 14/2

Radius = 7 units

Substituting the value of the radius and height, we have; V = π(7)²(11)

V = 1078.1 cubic units. Therefore, the volume of the cylinder is 1078.1 cubic units. Rounded off to one decimal place, the volume is 1078.1 cubic units.

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On Day 10, Kelly will have a total of 20 pennies in her penny jar.

To determine how many pennies Kelly will have on Day 10, we need to consider the progression of pennies added to her jar each day.

On Day 1, Kelly starts with 2 pennies. On Day 2, she adds 2 more pennies, resulting in a total of 2 + 2 = 4 pennies. This pattern continues, with 2 more pennies being added each day.

To find the number of pennies on Day 10, we can observe that the number of pennies on any given day can be calculated using the formula:

Number of pennies = Initial number of pennies + (Number of days - 1) * Number of pennies added per day

Using the provided information, we can substitute the values into the formula:

Number of pennies on Day 10 = 2 + (10 - 1) * 2

= 2 + 9 * 2

= 2 + 18

= 20

Therefore, on Day 10, Kelly will have a total of 20 pennies in her penny jar.

To summarize, starting with 2 pennies and adding 2 more pennies each day, Kelly will have a total of 20 pennies in her penny jar on Day 10.

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The point of intersection is (-1, 0). Therefore, the correct answer is C. (-1, 0).

To find the solution to the system of equations graphed below, we need to identify the point where the two lines intersect.

The equations of the lines are:

y = -x - 1

y = x + 1

To find the point of intersection, we can set the two equations equal to each other and solve for x:

-x - 1 = x + 1

Adding x to both sides:

-1 = 2x + 1

Subtracting 1 from both sides:

-2 = 2x

Dividing both sides by 2:

x = -1

Now that we have the x-coordinate, we can substitute this value back into either equation to find the y-coordinate. Let's use the second equation:

y = x + 1

y = -1 + 1

y = 0

Therefore, the point of intersection is (-1, 0).

Among the given options, the closest point to (-1, 0) is option C: (-1, 0).

Therefore, the correct answer is C. (-1, 0).

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The central angle of the sector is 540°.

The area of the sector formula is A = (1/2) r² θ Where, A = Area of sector r = Radius of sectorθ = Central angle of sector Given that the radius of the sector is 10mm and area is 40/3 pie mm²

To find the measure of central angle θ, plug the given values in the formula as shown; A = (1/2) r² θ40/3 pie = (1/2)(10)² θ40/3 pie = (1/2)100 θ40/3 pie = 50θ (multiply by 3/40)θ = (3/40) × 40πθ = 3π.

So, the measure, in degrees, of the central angle of the sector is;θ = (180/π) × 3πθ = 540°Therefore, the central angle of the sector is 540°.

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Annette Creighton opened Creighton Consulting and rented a small office space. She also hired a part-time worker to handle phone calls and make deliveries.

1. Annette Creighton decided to start her own consulting firm and named it Creighton Consulting.

2. As part of setting up the business, she began by renting a small office space. This would serve as the headquarters for her consulting operations.

3. To ensure smooth communication and timely deliveries, Annette realized the need for assistance. She hired a part-time worker to handle incoming phone calls and make necessary deliveries on behalf of the company.

4. The part-time worker would be responsible for answering the phone and addressing client inquiries or forwarding them to Annette if necessary. This step was crucial to maintaining good customer service and professionalism.

5. Additionally, the worker would also handle deliveries, ensuring that any documents, packages, or materials were transported promptly to clients or other relevant destinations.

6. By hiring a part-time worker, Annette aimed to streamline her operations and focus on core consulting tasks, such as client meetings, project management, and providing expert advice to clients.

7. The worker's role would involve effective communication skills, organization, and attention to detail to represent Creighton Consulting in a professional manner.

8. Annette understood that investing in administrative support would free up her time and allow the business to operate more efficiently, ultimately benefiting both her and her clients.

9. With the office space secured and the part-time worker in place, Annette was ready to embark on her consulting journey, confident in her ability to handle client inquiries and maintain smooth business operations.

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