Let us consider a circle of radius 2 cm. If an arc of this circle subtends an angle of 20 radian to the centre, then what is the length of the arc and area of the sector such formed?​

Answer:

Perpendicular.

Step-by-step explanation:

To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form

y = 2/3x - 4 ==> slope = 2/3

y = -3/2x - 7 ==> slope = -3/2

Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1

(2/3) * (-3/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular.

Therefore, the answer is: perpendicular.

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! :)

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

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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Answer: 52,400

Step-by-step explanation:

Answer:

Step-by-step explanation:

312

Answer:

36.92%

Step-by-step explanation:

180-132=48. Now we have to find 48 of 130 to find the percentage increase. 48 out of 130 = which equals 36.92.

The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.

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

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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(a) Total Number of Subsets of A:
In set theory, any set is a subset of itself. Additionally, the empty set is a subset of every set. As a result, there are 2^12 subsets of A.

Number of Subsets of A = 2^12 = 4096

(b) Number of Subsets of A having One or More Elements:
To find the number of subsets of A having one or more elements, we must subtract the empty set from the total number of subsets of A.
∴ Number of Subsets of A having One or More Elements = (2^12) − 1 = 4095

(c) Number of Subsets of A having Exactly One Element:
We can use the formula given below to compute the number of subsets of A having exactly one element. Here, n represents the number of elements in the set.

Formula: nC1 = n
∴ Number of Subsets of A having Exactly One Element = 12C1 = 12

(d) Number of Subsets of A having Two or More Elements:
Using parts (b) and (c), we can obtain the number of subsets of A having two or more elements by subtracting the number of subsets of A having exactly one element from the number of subsets of A having one or more elements.
∴ Number of Subsets of A having Two or More Elements = (2^12) − 1 − 12 = 4083.

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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.

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 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.

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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Answer:

y-intercept is (0,3) and the slope is 3

Step-by-step explanation:

Answer: the slope is 3x while 3 is the y-intercept.

Step-by-step explanation:

Answer:  What is this equation

Step-by-step explanation:

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!

Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

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

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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The population in the given scenario of a researcher randomly choosing 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together is all American families (option c).

In the given scenario, the population is all American families. The researcher has randomly chosen 1000 families from Kentucky to estimate the proportion of all American families who routinely eat dinner together. The researcher is using the sample of 1000 Kentucky families to make inferences about the population of all American families. By assuming that the sample is representative of the population, the researcher can use statistical methods to estimate the proportion of all American families who routinely eat dinner together. So, option C is the correct answer.

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Answer:11

Step-by-step explanation:

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

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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If a and b are any odd integers, then a2 + b2 is even.

And the proof for that we can explain as,

 So we have a and b are any odd integers. By definition of odd integer,

           a = 2r + 1 and b = 2r + 1 for any integers r and s.

By definition of odd integer,

          a = 2r + 1 and b = 2s + 1 for some integers r and s.

By substitution and algebra,

      a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.

        Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.

Proof: 1. Suppose a and b are any odd integers.

Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.

Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].

Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.

Proof:5. Hence a2 + b2 is even by definition of even.

Proof:6. Thus, a2 + b2 = 2k, where k is an integer.

  Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".

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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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The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and  the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708

a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:

mean of sample mean = mean of population = 1450 g/cm²

standard deviation of sample mean = standard deviation of population / square root of sample size

= 140 g/cm2 / √(10)

= 44.3 g/cm²

Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.

b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):

z = (x - mean of sample mean) / standard deviation of sample mean

= (1400 - 1450) / 44.3

= -1.13

Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:

P(z > -1.13) = 1 - P(z < -1.13)

= 1 - 0.1292

= 0.8708

Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.

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Answer:

45cm

Step-by-step explanation:

length × cross section = volume

in this case we call the unknown [tex]x[/tex]

so

[tex]x[/tex] x 110 = 4950

to get  [tex]x[/tex] you divide the volume by the cross section

[tex]\frac{4950}{110}[/tex]= [tex]x[/tex]

so [tex]x[/tex] = 45cm

The centre οf the circle is (-4, -11).

We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.

Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.

Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.

Let's separate the terms with x frοm the terms with y:

[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]

We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16

Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:

[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]

The equatiοn can nοw be written in standard fοrm:

[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]

The circle's centre is (-4, -11).

As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).

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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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She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.

The cost of lanterns is $6.50

Mrs Murphy bought 4 lanterns

Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26

The cost of banners is $5.25

Mrs Murphy bought 4 banners

Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21

Mrs Murphy bought 3 times as many balloons as she did lanterns

So, you multiply the number of lanterns bought (4) by 3

This gives 12

We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)

5.00 multiplied by 12 equals 60

Mrs Murphy bought 7 more garlands as she did lanterns

So, we add 7 to the number of lanterns bought (4)

7 plus 4 equals 11

To find the cost of the total garlands bought

We multiply the cost of each garland ($3.50) by the number of garlands bought (11)

3.50 multiplied by 11 equals 38.5

Now we can add up the costs of all the items

26+21+60+38.5=145.50

145.50 was the total amount she spent so we know it is the correct answer.

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Answer: 67

Step-by-step explanation:67 x1

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

The normal probability plot for the following sample deduce by z = (X - mean) / standard deviation as following steps.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The steps to calculate the z-percentiles for the given sample:

Find the mean of the sample:

mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16 = 1.235

Find the standard deviation of the sample:

First, find the sum of the squared differences between each observation and the mean:

(0.82 - 1.235)^2 + (0.88 - 1.235)^2 + (0.88 - 1.235)^2 + (1.06 - 1.235)^2 + (1.09 - 1.235)^2 + (1.14 - 1.235)^2 + (1.30 - 1.235)^2 + (1.33 - 1.235)^2 + (1.48 - 1.235)^2 + (1.50 - 1.235)^2 + (1.57 - 1.235)^2 + (1.64 - 1.235)^2 + (1.64 - 1.235)^2 + (1.70 - 1.235)^2 + (1.76 - 1.235)^2 + (1.83 - 1.235)^2 = 2.9878

Next, divide the sum by the sample size minus 1 and take the square root: standard deviation = sqrt(2.9878 / 15) = 0.4323

Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.

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To calculate the z-percentile for each observation in the sample.: Find the mean of the sample, Find the standard deviation of the sample and then use the formula z = (X - mean) / standard deviation.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The steps to calculate the z-percentiles for the given sample:

Find the mean of the sample:

mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16

mean = 1.235

Find the standard deviation of the sample:

First, find the sum of the squared differences between each observation and the mean:

(0.82 - 1.235)² + (0.88 - 1.235)² + (0.88 - 1.235)² + (1.06 - 1.235)² + (1.09 - 1.235)² + (1.14 - 1.235)² + (1.30 - 1.235)² + (1.33 - 1.235)² + (1.48 - 1.235)² + (1.50 - 1.235)² + (1.57 - 1.235)² + (1.64 - 1.235)² + (1.64 - 1.235)² + (1.70 - 1.235)² + (1.76 - 1.235)² + (1.83 - 1.235)² = 2.9878

Next, divide the sum by the sample size minus 1 and take the square root:

standard deviation = √(2.9878/15)

standard deviation = 0.4323

Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.

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