Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?

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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The total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

To calculate the total liabilities and stockholders' equity, we need to add the amounts of accounts payable, common stock, and retained earnings. Accounts Payable: The balance sheet provides the information that the accounts payable is $71,100.

Common Stock: The balance sheet states that the common stock is $70,000.

Retained Earnings: The balance sheet shows that the retained earnings are $134,300.

Calculate the total liabilities and stockholders' equity: Add the amounts of accounts payable, common stock, and retained earnings.

Total liabilities and stockholders' equity = Accounts payable + Common stock + Retained earnings

= $71,100 + $70,000 + $134,300

= $275,400

Therefore, the total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

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Answer:

- 15pr

Step-by-step explanation:

- 5p(3r) ← means multiply 3r by - 5p

= - 5p × 3r

= - 5 × 3 × p × r

= - 15 × pr

= - 15pr

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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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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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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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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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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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

After 8 visits: General Admission: Each person would pay $200. Annual Public Session Pass: Each person would pay $299.

After 10 visits: General Admission: Each person would pay $250. Annual Public Session Pass: Each person would still pay $299.

To determine when it is better to have a session pass versus just paying general admission, we need to compare the costs for each option.

General Admission with skate rental: $25

Annual Public Session Pass with skate rental: $299

After 8 visits:

For General Admission, the cost per visit would be $25 per visit.

Total cost for 8 visits: $25 x 8 = $200

For the Annual Public Session Pass, the cost is a one-time payment of $299, regardless of the number of visits. Therefore, after 8 visits, the cost remains the same at $299.

Therefore, after 8 visits, it would be more cost-effective to have the Annual Public Session Pass as the cost per person would be $299.

After 10 visits:

For General Admission, the cost per visit remains at $25 per visit.

Total cost for 10 visits: $25 x 10 = $250

For the Annual Public Session Pass, the cost remains the same at $299, regardless of the number of visits.

Therefore, after 10 visits, it would still be more cost-effective to have the Annual Public Session Pass as the cost per person would still be $299.

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The following question may be like this:

When is it better to have a session pass versus just paying general admission? After 8 visits: How much would each person pay? Show your work for calculations. Session Pass______? General Admission______?After 10 visits: How much would each person pay? Show your work for calculations.Session pass _____? General Admission_____?

GENERAL ADMISSION WITH SKATE RENTAL  $25

ANNUAL PUBLIC SESSION PASS WITH SKATE RENTAL $299

LOCKER RENTAL-ONE TIME USE  $5

HELMET RENTAL  $5

SKATE HELPER-PER HOUR $15

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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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:

F(5)= -1

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

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 density of lead is 11,300 kg/[tex]m^3[/tex], which means that lead is a dense material with a significant mass per unit volume.

To find the density of lead, we can use the formula:

Density = Mass / Volume

Given that the mass of lead is 3,390 kg and the volume is 0.3 [tex]m^3[/tex], we can substitute these values into the formula:

Density = 3,390 kg / 0.3[tex]m^3[/tex]

To simplify the calculation, we divide the mass by the volume:

Density = 11,300 kg/[tex]m^3[/tex]

Therefore, the density of lead is 11,300 kg/[tex]m^3[/tex].

Density is a physical property of a substance that describes how much mass is packed into a given volume. In this case, the density of lead tells us that for every cubic meter of lead, there are 11,300 kilograms of mass.

It is important to note that the density of lead is a characteristic property and remains constant regardless of the size or shape of the sample. It is a useful parameter in various scientific and industrial applications.

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The question probable may be:

If 3,390 kg of lead occupy a volume of 0.3 m^3, find the density of lead.

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

The value of the algebric  expression [tex]2^{-3} \cdot 3^{-2}$ is $\frac{1}{72}[/tex].

To compute the expression [tex]2^{-3} \cdot 3^{-2}[/tex], we can simplify each term separately and then multiply the results.

First, let's simplify [tex]2^{-3}[/tex]. The exponent -3 indicates that we need to take the reciprocal of the base raised to the positive exponent 3. Therefore, [tex]2^{-3} = \frac{1}{2^3} = \frac{1}{8}[/tex].

Next, let's simplify 3^{-2}. Similar to before, the exponent -2 means we need to take the reciprocal of the base raised to the positive exponent 2. So, [tex]3^{-2} = \frac{1}{3^2} = \frac{1}{9}[/tex].

Now that we have simplified both terms, we can multiply them together: [tex]\frac{1}{8} \cdot \frac{1}{9}[/tex]. When multiplying fractions, we multiply the numerators together and the denominators together. So, [tex]\frac{1}{8} \cdot \frac{1}{9} = \frac{1 \cdot 1}{8 \cdot 9} = \frac{1}{72}[/tex].

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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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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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Answer:

16cm

Step-by-step explanation:

perimeter for C is 44cm

perimeter for A and B 60cm

60cm-44cm=16cm

Hope this helps

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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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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Step-by-step explanation:

Therefore, the first five multiples of 17 are 17 , 34 , 51 , 68 and 85 .

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 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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2 5 7 ÷ 4 5 6 3

- 2 5 7

1993

- 1 7 9 9

Answer:

194

Answer:

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