A cylindrical garbage can has the dimensions shown.



A cylinder has a diameter labeled twelve inches and height labeled fifteen inches.
Question 1
Part A

What is the area of the horizontal cross section of the cylinder? Use 3.14
for π
.

Enter the correct answer in the box.

about
square inches
Question 2
Part B

What is the area of the vertical cross section of the cylinder through the centers of the bases?

Enter the correct answer in the box.

Answers

Answer 1

Check the picture below.

so the horizontal cross-section is simply the area of a circle with a radius of 6, and the vertical cross-section is simply a 12x15 rectangle.

[tex]\stackrel{ \textit{\LARGE horizontal cross-section} }{\pi (6)^2\implies 36\pi \implies 36(3.14)\implies \text{\LARGE 113.04}~in^2} \\\\\\ \stackrel{ \textit{\LARGE vertical cross-section} }{(12)(15)\implies \text{\LARGE 180}~in^2}[/tex]

A Cylindrical Garbage Can Has The Dimensions Shown.A Cylinder Has A Diameter Labeled Twelve Inches And

Related Questions

(a)
A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.
One possible selection:
Mon: Kung pao chicken
Tues: Beef with broccoli
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
A different selection:
Mon: Beef with broccoli
Tues: Kung pao chicken
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
(b)
Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?

Answers

There are 6 ways for the student to select her lunch when she chooses from the given main course selection and chooses between water or tea for her drink selection. 3 × 2 = 6 ways.

The problem is about counting the number of ways that can be possible to select the meal for the student.

The student selects one main course and one drink. The main course consists of one of the following:

beef with broccoli, moo shu pork, or chicken with cashew. She can select water or tea for her drink. Therefore, the total number of ways that can be possible to select her lunch is obtained by multiplying the number of options for each course.For instance, there are three options for main course selection, and two options for drink selection. Therefore, the total number of ways that she can select her lunch

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what 52,437 rounded to the nearest hundred

Answers

Answer: 52,400

Step-by-step explanation:

Please help me answer

Answers

1.a: In total, there are 380 people in the group, and 200 of them are men. The rest are women. We can set up the subtraction problem 380-200 and get 180 as a result. This means that THERE ARE 180 WOMEN.

We can check our work by adding 180 women and 200 men, and we get 380 as a result.

1.b: In total, there are 380 people. Since 130 of them voted for party b, we can set up the equation 380-130, and find out that there were 250 people who voted for party a. Since 120 of the people voting for party a are men, if we set up the equation 250-120, we can subtract the 120 men and find out only how many women voted for party a. THERE ARE 130 WOMEN VOTING FOR PARTY A, because 250-120=130.

2.a: There are 48 adults in total, and based on the pie chart showing adult’s favorite subjects, half of them chose English. We can find half of 48 by dividing it by 2. Since 48 divided by 2 is 24, 24 ADULTS CHOSE ENGLISH.

2.b: REESHMA IS WRONG. While one quarter of adults and one quarter of children chose maths, there were 48 adults were surveyed and only 32 children surveyed. One quarter of 48 is 12, but one quarter of 32 is only 8.

help me fast please I need good grades

Answers

A smaller sample size can offer a good estimate of the mean. The expressions population of working adults is not too vast to estimate the mean of the entire group using a sample.

What is expression ?

An expression in mathematics is a collection of numbers, variables, and complex mathematical (such as addition, subtraction, multiplied, division, multiplications, and so on) that express a quantity or value.

Expressions might be as basic as [tex]"3 + 4"[/tex] or as complicated as [tex]"(3x2 - 2) / (x + 1)"[/tex] . They may also contain functions like "sin(x)" or "log(y)".

Expressions can indeed be evaluated by swapping values for the variables and performing the algebraic calculations in the order specified.

If [tex]x = 2[/tex] , for example, the formula [tex]"3x + 5"[/tex] equals  [tex]3(2) + 5 = 11[/tex] . Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

If Fran chooses a random sample of the working adult population in her town, the mean for that group will most likely be close to the mean for the entire group.

Therefore,  A smaller sample size can offer a good estimate of the mean. The population of working adults is not too vast to estimate the mean of the entire group using a sample.

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A.14.5 square inches
B.29 square inches
c.20.5 square inches
d.32 square inches

Answers

Answer:

d. 32 in.²

Step-by-step explanation:

Bottom face: 6 in. × 0.5 inch

Side faces: 2 × 5 in. × 0.5 in.

Front and back faces: 2 x 6 in. × 4 in. / 2

surface area = 3 in.² + 5 in.² + 24 in.²

surface area = 32 in.²

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.

y=−6x ^2 +190x−826

Answers

As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.

What are a few selling price examples?

The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.

Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:

y' = -12x + 190

By setting y' to zero and figuring out x, we obtain:

-12x + 190 = 0

x = 15.83

The critical value of x is therefore 15.83.

We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:

y'' = -12

The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.

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Sophie bikes at the speed of s mph. Her friend rana is slower, her biking speed is only r mph. Today both girls went on 20 mile trip. Each girls was biking at there usual speed. How long did Sophie wait for rana at the finish line

Answers

The amount of time Sophie waited for Rana at the finish line can be calculated as 20/r - 20/s, where r is Rana's biking speed in mph and s is Sophie's biking speed in mph.

To find out how long Sophie waited for Rana at the finish line, we need to calculate the time it takes for each of them to complete the 20 mile trip. The time taken can be calculated using the formula: time = distance / speed.

Sophie's time to complete the trip can be calculated as follows:

time taken by Sophie = distance / speed of Sophie

time taken by Sophie = 20 / s

Similarly, Rana's time to complete the trip can be calculated as:

time taken by Rana = distance / speed of Rana

time taken by Rana = 20 / r

Since Sophie waits for Rana at the finish line, she would have to wait for the amount of time it takes for Rana to finish the trip. Therefore, the total waiting time would be the time taken by Rana to complete the trip minus the time taken by Sophie to complete the same trip:

waiting time = time taken by Rana - time taken by Sophie

waiting time = 20/r - 20/s

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If a matrix A is 5 x 3 and the product AB is 5 x 7, what is the size of B?

Answers

The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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stuck on this question need some help

Answers

Answer:

1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).

2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).

3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).

Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?​

Answers

Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.

1 minute = 60 seconds

4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds

So, Michaela's rate is:

distance / time = x / 290 seconds

where x is the distance she can swim in 290 seconds.

Simplifying the equation:

x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance

We know that Michaela can swim 500 meters in 290 seconds:

500 meters / 290 seconds = 1.724 meters per second

Therefore, in 10 minutes (600 seconds), she will swim:

distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters

So, Michaela will swim 1034.4 meters in 10 minutes.

Step-by-step explanation:

Peter buys 30 apples at R5. 00 each. He sell each apple for R7. 0. How much profit does he makes?

Answers

Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.

To calculate his earnings, we subtract his price from his revenue.

profit = revenue - cost

In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.

Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.

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Help me please
For problems 4-9,find the circumference.Round your answer to the nearest hundredth.Use 3.14 for п

Answers

The circumference of circle has the formula 2xPixr

where, r = radius of circle.

The relation between radius (r) and diameter (d) of the circle is d = 2r

Circumference = pi x diameter = 3.14 x 25m = 78.5m

Circumference = 2 x pi x radius = 2 x 3.14 x 4.5cm = 28.26cm

Circumference = 2 x pi x radius = 2 x 3.14 x 28in = 175.84in

Circumference = pi x diameter = 3.14 x 19ft = 59.66ft

Circumference = 2 x pi x radius = 2 x 3.14 x 3mm = 18.84mm

Circumference = 2 x pi x radius = 2 x 3.14 x 35in = 219.8in

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A champion race horse can run 10 000 metres in 60 minutes. What is the average speed in km/h 10,000.show working out.
a champion racehorse runs 10000 metres in 60 minutes what is the average speed in km/h show working out ​

Answers

Answer: We have one km being covered in one minute. So how many km do we cover in one hour? Remember, there are 60 minutes in one hour. Do you think it might be 60 km in one hour? Can you say that a different way, say number of km in one hour? 60 km in one hour. Close. Very good. Now let’s clean up your answer and just say 60 km per hour or 60 ``````````````````````.

Is the following an isosceles trapezoid?



A. No, the bases are parallel, but the legs are not congruent.


B. No, the bases are not parallel and the legs are not congruent.


C. Yes, the bases are parallel and the legs are congruent.


D. Yes, all 4 sides are parallel.

Answers

The answer is C. Yes, the bases are parallel and the legs are congruent.

What is trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. There are different types of trapezoids, including isosceles trapezoids where the legs are congruent and right trapezoids where one of the angles between a leg and a base is a right angle. A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs. The legs can be either congruent or non-congruent.

There are several types of trapezoids, based on the relationships between their sides and angles:

Isosceles trapezoid: This is a trapezoid where the legs are congruent. The bases may or may not be congruent.

Right trapezoid: This is a trapezoid where one of the angles between a leg and a base is a right angle (90 degrees).

Scalene trapezoid: This is a trapezoid where none of the sides are congruent.

Trapezium: In British English, a trapezium is a quadrilateral with no parallel sides. In American English, this shape is called a general quadrilateral.

Trapezoids are used in many areas of mathematics, including geometry and calculus. In geometry, they can be used to calculate the area and perimeter of various shapes. In calculus, they can be used to calculate integrals over regions with curved boundaries.

Here,

In an isosceles trapezoid, the legs (non-parallel sides) are congruent, and the bases (parallel sides) are also congruent.

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for the theoretical exponential distribution with a scale of 7, calculate and report the mean, median, standard deviation, and probability of a wheelchair not needing to be serviced for the 16 weeks of the semester.

Answers

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

What's exponential distribution

The exponential distribution is a continuous probability distribution that describes the time between two consecutive events that occur randomly and independently of each other. This distribution is useful in the fields of reliability, physics, and finance, among others.

The exponential distribution has a single parameter known as the scale parameter, which is denoted by lambda (λ) and is typically expressed in terms of the mean time between failures.The mean, median, and standard deviation are three of the most common summary statistics used to describe a probability distribution.

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester can also be calculated using the exponential distribution.

Mean: The mean of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the mean is 1/λ = 1/0.143 = 6.993.

Median: The median of the exponential distribution is equal to ln(2)/λ.λ = 1/7 = 0.143

Therefore, the median is ln(2)/λ = ln(2)/0.143 = 4.837.

Standard deviation: The standard deviation of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the standard deviation is 1/λ = 1/0.143 = 6.993.

Probability: P(X > 16) = e^(-λx)λ = 1/7 = 0.143X = 16P(X > 16) = e^(-0.143 * 16) = 0.230

Therefore, the probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

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Solve for x to the nearest tenth.
8
3
4
7

Answers

Answer:

x=4.9

Step-by-step explanation:

using the Pythagorean theorem to find the leg of tringle A:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]y^{2} +3^{2} =7^{2}[/tex]

[tex]y^{2} +9=49\\y^{2} =40\\\sqrt{y^{2} } =\sqrt{40} \\y=\sqrt{40}[/tex]

we know that the hypotenuse for tringle B is [tex]\sqrt{40}[/tex] so, now we can find the value of x:

using the Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]4^{2} +x^{2} =(\sqrt{40} )^{2}[/tex]

[tex]16+x^{2} =40\\x^{2} =24\\\sqrt{x^{2} } =\sqrt{24} \\x=4.9[/tex]

Blowlers that score at least 228 point will make it to the next round

Answers

Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

What is the answer to this math problem? I can’t seem to figure it out.

Answers

Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

Solve the given differential equation by undetermined coefficients.y" - 8y' +16y = 24x +2

Answers

The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.

To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:

The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).

Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.

Substituting this form into the differential equation, we get:

y_p" - 8y_p' + 16y_p = 24x + 2

Taking the derivatives and plugging them back into the equation, we get:

-8A + 16B + 16C = 2

0 + 0 + 16C = 24

Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.

Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.

The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.

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A rectangular pyramid has a volume of 100 cm? What is the volume of a rectangular prism in cubic centimeters with the same dimensions?

Answers

The volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.

What is rectangular prism?

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape with six rectangular faces, where each pair of opposite faces are congruent (i.e., have the same dimensions) and parallel to each other.

The rectangular prism is defined by three dimensions: length, width, and height. The length is the longest dimension of the prism, the width is the second-longest dimension, and the height is the shortest dimension, perpendicular to both length and width. The volume of a rectangular prism is given by the formula: V = l * w * h.

In the given question,

Let's assume that the rectangular pyramid has a rectangular base with length l, width w, and height h. The formula for the volume of a rectangular pyramid is given by:

V_pyramid = (1/3) * base_area * height

where base_area = l * w is the area of the rectangular base of the pyramid.

We know that the volume of the rectangular pyramid is 100 cm^3, so we can write: 100 = (1/3) * l * w * h

Simplifying this equation, we get:

l * w * h = 300

Now, let's find the volume of the rectangular prism with the same dimensions. The formula for the volume of a rectangular prism is given by: V_prism = base_area * height

where base_area = l * w is the area of the rectangular base of the prism.

Since the rectangular prism has the same dimensions as the rectangular base of the pyramid, its volume is given by: V_prism = l * w * h

Substituting the value of l * w * h from the equation we derived earlier, we get: V_prism = 300

Therefore, the volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.

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One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes. What part of the bag can they eat together in the given time? 1 minute. 2 minute, and 3 min

Answers

the two cats can eat 1/6 of the bag in one minute, 1/3 of the bag in two minutes, and 1/2 of the bag in three minutes.

Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

A. x/4 +1= -3 B. x +4= -12 How can we get equation b from equation a? A. Add/subtract the same quantity to/from both sides B. Add/subtract a quantity to/from only one side C. Multiply/divide both sides by the same non-zero constant D. Multiply/divide both sides by the same variable expression

Answers

Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.  

What are some integers non-constant?

If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).

As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.

Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:

[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]

We obtain x = -16 by multiplying both of the equation's sides by 4.

Starting with the variable with one of the equation's equations, we can solve equation B for x:

[tex]x + 4 = -12[/tex]

Therefore, We obtain [tex]x = -16[/tex] by deducting  [tex]4[/tex] from both of the equation's components.

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QUESTION 5
What portion of a whole does two sevenths of five ninths represent?

Answers

Answer:

10/63

Step-by-step explanation:

Equation: 2/7 * 5/9

Multiply the numerators: 2*5=10

Multiply the denominators: 7*9=63

Your answer: 10/63

difference between repeating & terminating decimal

Answers

Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Step-by-step explanation:

I hope that this helped! :)

Greg sold small boxes of candy for $3 and
large boxes for $5. He sold a total of 21
boxes for $87. How many large boxes did he sell?

Answers

Answer:

12 large boxes, 9 small boxes

Step-by-step explanation:

Let s = number of small boxes

l = number of large boxes

We set up and solve this system of equations:

s + l = 21------->3s + 3l = 63

3s + 5l = 87------>3s + 5l = 87

----------------

2l = 24

l = 12, s = 9

A sandwich shop owner observed the first 100 sandwich orders of the day. The data that the owner obtained is given in the table.


Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15


Which of the following circle graphs correctly represents the data in the table?
a circle graph with four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent
a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent
a circle graph with four sections, labeled chicken 30 percent, vegetarian 20 percent, turkey 35 percent, and ham 15 percent
a circle graph with four sections, labeled ham 30 percent, chicken 20 percent, vegetarian 35 percent, and turkey 15 percent
Question 6(Multiple Choice Worth 2 points)

Answers

The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"

The correct answer choice is option B.

Which of the following circle graphs correctly represents the data in the table?

Type of Sandwich Number of Customers

Vegetarian 30

Turkey 20

Ham 35

Chicken 15

Total number of customers = 30 + 20 + 35 + 15

= 100

Percentage of each sandwich:

Vegetarian = 30/100 × 100

= 30%

Turkey = 20/100 × 100

= 20%

Ham = 35/100 × 100

= 35%

Chicken = 15/100 × 100

= 15%

Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.

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the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20. How many students use this lunch line?

Select the answers from the drop-down list to correctly complete the sentence

There are ___ students ___ that use this lunch line

1. 142
2. 62
3. 36
4.35

1. or more
2. or fewer ​

PLEASE HELP NEEDED!!!

Answers

The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.

What is Equation?

An equation is  mathematical statement that shows  equality of two expressions, typically separated by  equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of  real-world scenario or problem in mathematical terms.

The variables in equation can take on different values, and  equation remains true regardless of the values chosen for  variables. Solving  equation means finding  values of the variables that make  equation true.

Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.

There are 155 students or more students that use this lunch line.

The correct answer is 1. or more.

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How can I use the compound angle formula to write sin 165degrees as surds?

Answers

We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...

Trigonometric identities enable the expression of sin 165° as,

Sin (15°) = sin(180° - 165°)

(-sin 180 + -sin 165) = -sin 345

cos(-75°) = cos(-90° - 165°)

(90 + 165)/255 = -cos 255

Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.

165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.

Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.

525 is a positive number of interactions angle, while 195 is a negative coterminal angle.

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sebi rides his bike at a constant rate of 10 mph by a linear equation to represent how far he travels

Answers

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

what is linear equation ?

The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.

given

Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:

Distance is determined by rate and duration.

When we change the numbers, we obtain:

d = 10t

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

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Andrew can row his boat downstream 15 miles in the same amount of time as it takes him to row upstream 8 miles. If the current in the river is 2 mph, how fast can Andrew row in still water? (round to the tenth)
hint: t=d/t​

Answers

The time that Andrew can use to row his boat in still waters would be = 5.75 hrs.

How to calculate the speed of the boat in still water?

The speed can be defined as the scalar quantity that shows that amount of distance that is covered with respect to time.

The formula that can be used to calculate speed = distance/time.

The speed of the current in the river = 2 mph

The distance covered downstream = 15miles

The distance covered upstream = 8

average distance = 15+8/2 = 11.5 miles

Given 2 miles = 1 HR

11.5 miles = X

Make X the subject of formula;

X = 11.5×1/2

= 5.75 hrs

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