work out minimum and maximum number of hikers who could have walked between 7 miles and 18 miles

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:

1. Calculate the derivatives of x(t) and y(t) with respect to t:

dx/dt = 6t
dy/dt = 3t^2

2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2

3. Set the slope equal to 1/2 and solve for t:

t/2 = 1/2
t = 1

4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:

x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

To learn more about coordinates, refer below:

https://brainly.com/question/16634867

#SPJ11

Answer:

1 candy bar is $1.25

2 candy bars is $2.50

3 candy bars is $3.75

4 candy bars is $5

Equation:

y = 1.25x

y being the cost and x being number of candy bars

The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹

From the question, we are to write the given expression using a single, positive exponent

From the given information,

The given expression is

14⁻³ · 14¹²

This means

14⁻³ × 14¹²

To solve this, let us revise some of the laws of indices

Thus,

The expression

14⁻³ × 14¹²

can be written as

14⁻³ ⁺ ¹²

14⁹

Hence, the expression written as a single exponent is 14⁹

Learn more on Rewriting an expression here: https://brainly.com/question/29259390

#SPJ1

If each locker is identified by one letter and one digit, the total number of lockers built in the school is 229.

There are 26 letters in the alphabet (A to Z), and if each locker is identified by one letter and one digit, then there are a total of 26 × 10 = 260 possible locker identifications using the letters A to Y and digits 0 to 9.

Out of these, there are 4 digits used to identify the lockers with the letter Z. So, there are 10 − 1 = 9 digits left to use for the remaining lockers, as we cannot use the digit already used for the lockers with the letter Z.

Similarly, there are 25 letters left to use for the remaining lockers, as we cannot use the letter Z.

Therefore, the number of remaining lockers is 9 × 25 = 225. Adding the 4 lockers with the letter Z, the total number of lockers built in the school is 225 + 4 = 229.

To learn more about digits, click here:

https://brainly.com/question/30142622

#SPJ11

Answer:

250+25d= P

Step-by-step explanation:

How to say it aloud: "$250 plus 25 times miles ran is equal to total amount earned"

250 is a fixed amount that is apart of the equation. In order to get a correct total at the end, $250 must be added to 25d.

25d stands for $25 times the amount of miles ran, which according to the word problem is represented by d. The reason we multiply 25 times d is because Marcus is getting $25 for every mile he runs. At the end of his run, we need to multiply $25 by those miles.

The reason everything equals P is because according to the word problem, P is the amount of money earned.

I hope that makes sense.

Answer:

Obese

Step by Step Explanation:

looked it up :)

Step-by-step explanation:

Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:

x - (-9/14) = 17/28

Simplifying the left-hand side:

x + 9/14 = 17/28

Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:

28(x + 9/14) = 28(17/28)

Simplifying:

4(2x + 9) = 17

Expanding:

8x + 36 = 17

Subtracting 36 from both sides:

8x = -19

Dividing by 8:

x = -19/8

Therefore, the other rational number is -19/8.

Deloria is analyzing the relationships between relative frequencies of nuts.

She has found that the relative frequency of a specific type of nut is 15%, which is calculated by dividing the number of that nut (3) by the total number of nuts (30).

Deloria might be comparing this relative frequency to other types of nuts to determine their prevalence or importance in a given context.

To calculate the relative frequency, we can divide the number of occurrences of the specific nut (3) by the total number of nuts (30):

Relative frequency = (Number of occurrences of specific nut) / (Total number of nuts)

Relative frequency = 3 / 30 = 0.1 = 10%

Therefore, the relative frequency of the specific type of nut is 10%, not 15%. It seems there was an error in the initial statement.

By analyzing relative frequencies, Deloria can compare the prevalence or importance of different types of nuts in a given context.

By calculating and comparing the relative frequencies of different types of nuts, Deloria can gain insights into the distribution and significance of each nut type within the dataset or sample.

To learn more about insights, refer below:

https://brainly.com/question/30458271

#SPJ11

The area enclosed by the figure at the right is 2856 square meters.

To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.

To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:

1600 + 1256 = 2856 square meters

Therefore, the area enclosed by the figure at the right is 2856 square meters.

Learn more about area,

https://brainly.com/question/28470545

#SPJ11

The sum of the heights of the two trees with given volumes and radius is equal to  9 cm (nearest whole number ).

Volumes of the cylindrical trunks of first tree = 904.78 cm³

and Volumes of the cylindrical trunks of first tree =113 cm³.

radius of the  first tree = 6cm

Radius of the second tree = 6cm

The formula for the volume of a cylinder is V = πr²h,

where r is the radius of the cylinder,

h is the height of the cylinder,

and π is the constant approximately value equal to 3.14.

For the first tree,

⇒904.78 = π(6)²h

⇒h = 904.78 / (π(6)²)

⇒h ≈ 8.004 cm

For the second tree, we have,

⇒113 = π(6)²h

⇒h = 113 / (π(6)²)

⇒h ≈ 0.9996 cm

This implies,

The sum of the heights of the two trees is equal to,

= 8.004 + 0.9996

= 9.003 cm

= 9 cm ( nearest whole number)

Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.

learn more about height here

brainly.com/question/24028597

#SPJ4

The given question is incomplete, I answer the question in general according to my knowledge:

The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and  another one with radius 6cm and volume 113 cm³.

What is the sum of the heights of the two trees? Round your answer to the nearest whole number

The cost of an adult ticket is $9 and the cost of a student/child ticket is $7. The solution was found by solving a system of two equations, where the variables x and y represent the costs of the two types of tickets.

Let's assign variables for the unknowns

x = cost of adult tickets

y = cost of student/child tickets

From the given information, we can create two equations

Equation 1 Friend, mom, and little sister paid a total of $23

x + 2y = 23

Equation 2 Another family paid $39 for two adults and three students

2x + 3y = 39

We now have two equations with two unknowns, which we can solve using substitution or elimination.

Here, using substitution

Solve for x in Equation 1

x = 23 - 2y

Substitute the value of x into Equation 2

2(23 - 2y) + 3y = 39

Simplify and solve for y

46 - 4y + 3y = 39

-y = -7

y = 7

Substitute the value of y into Equation 1 to solve for x

x + 2(7) = 23

x = 9

Therefore, the cost of adult tickets is $9 and the cost of student/child tickets is $7.

To know more about Substitution method:

https://brainly.com/question/30284922

#SPJ4

The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.

We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.

Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.

To know more about temperature, refer to the link below:

https://brainly.com/question/8823320#

#SPJ11

The probability of Henry choosing a Milky Way and then a Snickers is 2/27.

1. First, let's find the total number of candy pieces in Henry's candy jar:
3 Snickers + 1 Reese's + 1 Twix + 2 Milky Ways + 2 Skittles Packs = 9 pieces of candy.

2. Next, we'll calculate the probability of choosing a Milky Way on the first pick:
There are 2 Milky Ways and 9 total pieces of candy, so the probability is 2/9.

3. Since Henry puts the candy back, there are still 9 pieces of candy for the second pick. Now, we'll calculate the probability of choosing a Snickers on the second pick:
There are 3 Snickers and 9 total pieces of candy, so the probability is 3/9 (or 1/3).

4. Finally, we'll multiply the probabilities of each individual event to find the probability of both events occurring together (choosing a Milky Way and then a Snickers):
(2/9) * (1/3) = 2/27

So, the probability of Henry choosing a Milky Way and then a Snickers is 2/27.

Learn more about probability,

https://brainly.com/question/25870256

#SPJ11

The old coordinates are;

W (3, 14)

Y (12, 14)

X (6, 11)

While the new coordinates for the reflected triangle are:

W'' (3, -14)

X'' (6, -11)

Y'' (12, -14).

See the attached image.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.

A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.

Learn more about Reflection:
https://brainly.com/question/29093485
#SPJ1

Answer:

First Problem:

Transformation: Reflection across the x-axis, shift 2 units rightward

Equation: g(x)=-5^(x-2)

Second Problem:

Transformation: Reflection across the y-axis, shift 4 units upward

Equation: 10^-x+4

Step-by-step explanation:

Imagine folding a piece of paper and using the x or y axis as the crease marks. By folding them and comparing them, we can find out whether it is either the x-axis, y-axis, or both-axis. Then, we move the graph, to match the position in the second picture.

As for equations, exponential functions have the parent function of y=b^(x+c)+h. By plugging in any points given, let's say (1,5), we can see that 5=b^1 and simplifying shows 5=b. Therefore, the function is y=5^x. Using that first equation, we transform it. If over the x-axis, convert y=b^x to y=-b^x. If over the y-axis, convert y=b^x to y=b^-x. For horizontal shift, if going rightward, it is x-c. If going leftward, it is x+c. For vertical shift, if going up, b^x+h. If going down, b^x-h.

If unsure, plug-in points to see if your answer checks out with the equation :)

Ms. Brock can now fill up to 88 spray bottles with her preparation.

It is calculated that:

hence we have that

1 gallon = 128 fluid ounces

1 pint = 16 fluid ounces  

cross multiplying

16 fluid ounces x 1 gallon = 128 fluid ounces x 1 pint

1 gallon = (128 fluid ounces x 1 pint) / 16 fluid ounces

1 gallon = 8 pints

Consequently, there are 8 pints in one full gallon.

Ms. Brock blended 1 gallon of cleaner with 10 gallons of water, thus resulting in 11 gallons.

To figure out the total number of pints Ms. Brock has in her solution, we must multiply 11 gallons by 8 pints/gallon:

11 gallons x 8 pints/gallon = 88 pints

Learn more about word problem at

https://brainly.com/question/21405634

#SPJ1

This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices

In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.

To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.

To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.

To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.

In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.

This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.

To know more about algorithm refer here

https://brainly.com/question/31936515#

#SPJ11

The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40

Multiply the three probabilities in order to get the compound probability:

Probability = favorable outcome / total number of outcome

Probability of getting an odd number

favorable outcome = 5

Total number of outcome = 10

P(odd number)= 5/10 = 1/2

Probability of not getting filling head  

Favorable outcome = 1

P( not flipping heads)= 1/2  

Probability of not getting a 6

favorable outcome = 9

P(not spinning a 6)= 9/10

= 1/2×1/2×9/10

= 9/40

The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40

To know more about probability click here :

https://brainly.com/question/30034780

#SPJ4

The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.

Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.

Learn more about integral here:

brainly.com/question/28384037

#SPJ11

The limit of (sin(9x))/x as x approaches 0 is equal to 9.

To evaluate this limit analytically, we can use L'Hopital's Rule.

Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.

Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.

We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.

For more similar questions on topic limit analytically

brainly.com/question/13641622

#SPJ11

The problem involves finding the marginal cost of producing a certain number of DVD players, given the total cost function. Specifically, we are given the total cost function C(x) = 120 + 3x^2-3, where x is the number of DVD players produced, and we need to find the marginal cost when x = 3.

To find the marginal cost, we need to take the derivative of the total cost function with respect to x and evaluate it at x = 3. The marginal cost represents the cost of producing one additional unit of the product, and is an important concept in economics and business.

Understanding the relationship between marginal cost and production volume is crucial for optimizing production and pricing decisions for companies. Marginal cost analysis is used extensively in many fields, including manufacturing, finance, and marketing.

For more similar questions on topic Marginal cost.

https://brainly.com/question/17230008

#SPJ11

Answer:

Step-by-step explanation:

The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.

Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.

To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,

so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.

Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.

Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.

To know more about juice boxes refer here:

https://brainly.com/question/19751489#

#SPJ11

Waterways Corporation's budget for Q1 2022 involves sales, inventory, materials, labor, overhead, expenses, and financing.

Waterways Corporation is preparing its budget for the first quarter of 2022. The company has gathered information from its managers to begin the budgeting process.

The company expects unit sales to be 112,000 in November 2021, 104,000 in December 2021, and 113,000 in January 2022. The company also expects to keep 10% of next month's unit sales in ending inventory. The company collects 85% of Accounts Receivable in the month of sale and 15% in the month after sale.

Raw materials cost 80 cents per pound, and two pounds of direct materials are required to produce each unit. The company likes to keep 5% of the materials needed for the next month in its ending inventory.

Labor requires 12 minutes per unit, paid at a rate of $9 per hour. The company has variable selling and administrative costs of $1.60 per unit, including advertising, insurance, salaries, and depreciation. The company also plans to make a $480,000 equipment purchase in February.

The company's cash balance on December 31, 2021, was $99,000, but the management wants to maintain a cash balance of at least $700,000 starting on January 31, 2022. The company pays dividends each month at the rate of $2.70 per share for 4,610 shares outstanding.

The company has an open line of credit with Romney's Bank with borrowing terms of $1,000 increments at 9% interest. The company borrows on the first day of the month and repays on the last day of the month.

Learn more about Waterways Corporation

brainly.com/question/30681939

#SPJ11

The range of x values between which a zero can be found is -9/4 < x < -4.

Since x + 4 and 4x + 9 are linear factors of the quadratic expression, the quadratic expression can be written as:

Q(x) = k(x + 4)(4x + 9)

where k is some constant.

To find the values of x for which Q(x) = 0, we can set each factor equal to zero and solve for x:

x + 4 = 0 --> x = -4

4x + 9 = 0 --> x = -9/4

Therefore, the zeros of Q(x) are x = -4 and x = -9/4.

To find the range of x values between which a zero can be found, we need to determine the sign of Q(x) in each of the three intervals:

1. x < -9/4

2. -9/4 < x < -4

3. x > -4

For x < -9/4, both x + 4 and 4x + 9 are negative, so Q(x) = k(negative)(negative) = k(positive), which is positive.

For x > -4, both x + 4 and 4x + 9 are positive, so Q(x) = k(positive)(positive) = k(positive), which is also positive.

For -9/4 < x < -4, x + 4 is positive and 4x + 9 is negative, so Q(x) = k(positive)(negative) = k(negative), which is negative.

Therefore, the range of x values between which a zero can be found is -9/4 < x < -4.

Learn more about quadratic equations:

brainly.com/question/30098550

#SPJ4

To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.

For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:

1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.

2. Ramp rise: In this case, the rise is 15 inches.

3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.

15 inches x 12 = 180 inches

4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.

5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.

To know more about ADA specifications refer to

https://brainly.com/question/30286625

#SPJ11

If both belts are​ used, it will take 2.25 minutes to move the cans to the storage area

To solve this problem, we need to use the concept of rate of work. We know that the larger belt can move 200 pounds of aluminum in 3 minutes, which means its rate of work is 200/3 = 66.67 pounds per minute. Similarly, the smaller belt can move the same quantity of cans in 9 minutes, which means its rate of work is 200/9 = 22.22 pounds per minute.

When both belts are used together, their rates of work add up, so the total rate of work is 66.67 + 22.22 = 88.89 pounds per minute. We can use this rate of work to find how long it will take to move the cans to the storage area.

Let's assume that it takes x minutes to move the cans using both belts. Then, we can set up the following equation:

88.89x = 200

Solving for x, we get:

x = 2.25 minutes

Therefore, it will take 2.25 minutes to move the cans to the storage area using both belts.

Learn more about rate of work here: https://brainly.com/question/31245785

#SPJ11

a. FA5.6₁₆ = 15x16² + 10x16 + 5 + 6/16 = 4005.375₁₀

b. 725.38₁₀ remains the same in decimal form

c. 3F4.8₁₆ = 3x16² + 15x16 + 4 + 8/16 = 1012.5₁₀

d. 73.25₈ = 7x8 + 3 + 2/8 = 59.3125₁₀

e. FF.F0₁₆ = 15x16 + 15 + 15/16 + 0/256 = 255.9375₁₀

Decimal form is a way of representing numbers using the base 10 number system. In this system, there are 10 digits from 0 to 9 that are used to represent all possible numbers. Each digit in a decimal number has a place value that is determined by its position. The rightmost digit represents units, the next digit to the left represents tens, and so on, with each successive digit representing higher powers of 10.

Learn more about decimal form:

https://brainly.com/question/16361602

#SPJ4

The crop sizes for first 4 years without using fertilisers are:

The size of the potato crop for each of the first four years is computed as follows:

For Year 1:

= 15 tonnes * 1

= 15 tonnes

For Year 2:

= 15 tonnes x 0.8

= 12 tonnes

For Year 3:

= 12 tonnes x 0.8

= 9.6 tonnes

For Year 4:

= 9.6 tonnes x 0.8

= 7.68 tonnes

Read more about Size

brainly.com/question/27434334

#SPJ1