A
circle has a circumference of 12. It has an arc of length 11.
What is the central angle of the arc, in degrees?

The volume of the figure is: V = 8,568 m³. The correct option is O 8,568 m³.

To find the volume of the given figure, we can use the formula for the volume of a rectangular prism which is V = lwh,

where,

l is the length,

w is the width and

h is the height of the prism.

Given dimensions:

Length (l) = 21 m

Width (w) = 17 m

Height (h) = 24 m

Cuboid volume formula:

V = lwh

Insert the given values ​​for length (l), width (w), and height (h):

l = 21 m

w = 17 m

h = 24 m

Substitute the values ​​into the formula:

V = 21 m × 17 m × 24 m

Multiply the values:

Therefore, the volume of the figure is: V = lwhV = 21 m × 17 m × 24 mV = 8,568 m³Hence, the correct option is O. 8,568 m³.

For more questions on volume

https://brainly.com/question/28058531

#SPJ8

Answer:

its 6

Step-by-step explanation:

divided 12 with 2 and divided 30 with 5

Answer:

-50/7

Step-by-step explanation:

I dont know what u want me to do but this is what happens when u evaluate it

the amount of work done in each situation given below :-

a. Work done = force x distance = 150 N x 3 m = 450 J
b. Work done = force x distance x cos(theta) = mgh = 40 kg x 9.8 m/s^2 x 40 m x cos(50°) = 1,715.5 J
c. Work done = force x distance x cos(theta) = 140 N x 250 m x cos(20°) = 3,183 J
d. Work done = force x distance x cos(theta) = 100 N x 500 m x cos(45°) = 35,355 J
e. No work is done as the book is not moving and the table is not being displaced.
a. Work done = force x distance x cos(theta). Here, force = 150 N, distance = 3 m, and theta = 0° (since the force is against friction, we can assume it's horizontal). Work done = 150 x 3 x cos(0) = 450 J.

b. Work done = force x distance x cos(theta). Here, force = mg (mass x gravity) = 40 kg x 9.81 m/s² = 392.4 N, distance = 40 m, and theta = 50°. Work done = 392.4 x 40 x cos(50) ≈ 10,090 J.

c. Work done = force x distance x cos(theta). Here, force = 140 N, distance = 250 m, and theta = 20°. Work done = 140 x 250 x cos(20) ≈ 32,899 J.

d. Work done = force x distance x cos(theta). Here, force = 100 N, distance = 500 m, and theta = 45°. Work done = 100 x 500 x cos(45) ≈ 35,355 J.

e. In this situation, the force acting on the book is zero because the book is sitting on the table and not being directly pushed by the student. Therefore, the work done on the book is 0 J.

Visit here to learn more about work done  : https://brainly.com/question/30073908
#SPJ11

To graph y = x² + 4x + 6 with 5+ points using an x/y chart, follow these steps:

Step 1: Create an x/y chart with five rows and two columns. Label the first column x and the second column y.

Step 2: Choose five values for x. You can choose any values you want as long as you plug them into the equation in the next step. In this example, we will use -3, -2, -1, 0, and 1. Write these values in the first column of your chart.

Step 3: Plug each value of x into the equation y = x² + 4x + 6 to find the corresponding value of y. Write these values in the second column of your chart. To make it simpler, here are the calculations for each point:When x = -3: y = (-3)² + 4(-3) + 6 = 3When x = -2: y = (-2)² + 4(-2) + 6 = 2When x = -1: y = (-1)² + 4(-1) + 6 = 1When x = 0: y = (0)² + 4(0) + 6 = 6When x = 1: y = (1)² + 4(1) + 6 = 11

Step 4: Plot each point on the x/y chart. The x value goes on the horizontal axis (x-axis) and the y value goes on the vertical axis (y-axis). Once you have plotted all five points, connect them with a smooth curve to create the graph of y = x² + 4x + 6. The graph is shown in the figure below.

For more questions on: graph

https://brainly.com/question/29538026

#SPJ8

Answer:

405

Step-by-step explanation:

Answer: 405

Step-by-step explanation:

This system of equations is inconsistent because there is no solution that satisfies both equations simultaneously. Therefore, there is no value of x and y that satisfies the given conditions.

To find the values of x and y in the sequence 1, 2, x, 5, y, 8, given that the resulting number is 5 and the mean is 4, we can use the concept of the mean.

The mean is calculated by summing all the numbers in a sequence and dividing by the total count. In this case, the mean is given as 4.

The sum of the numbers in the sequence is 1 + 2 + x + 5 + y + 8. We need to find the values of x and y such that the resulting number is 5 when added to the sequence.

Using the mean formula, we can set up the equation:

(1 + 2 + x + 5 + y + 8) / 6 = 4

Simplifying this equation, we have:

(16 + x + y) / 6 = 4

Multiplying both sides of the equation by 6, we get:

16 + x + y = 24

Rearranging the equation, we have:

x + y = 8

Since the resulting number is 5 when added to the sequence, we can write:

1 + 2 + x + 5 + y + 8 = 5

Simplifying this equation, we get:

x + y = -11

Now, we have a system of equations:

x + y = 8

x + y = -11

This system of equations is inconsistent because there is no solution that satisfies both equations simultaneously.

For more such questions on inconsistent visit:

https://brainly.com/question/15654281

#SPJ8

The deductible amount of investigation expenses related to expanding her hotel chain into another city is $25,000, and the deductible amount of investigation expenses related to opening a restaurant is $184,400.

For the investigation expenses related to expanding her hotel chain, the entire amount of $25,000 can be deducted in the current year since Henrietta decided not to proceed with the expansion. Regarding the investigation expenses related to opening a restaurant, the deductible amount needs to be determined. Since the restaurant began operations on May 1, we need to calculate the deductible amount for the period from January 1 to April 30. To calculate the deductible amount for the restaurant investigation expenses, we divide the total expenses of $553,200 by 12 months to get the per-month amount. Rounded to the nearest dollar, the per-month amount is $46,100. Next, we multiply the per-month amount by the number of months from January 1 to April 30, which is 4 months. Deductible amount for the restaurant investigation expenses = $46,100 * 4 = $184,400. Therefore, Henrietta can deduct $184,400 for the investigation expenses related to opening the restaurant.

Learn more about deductible amount here:

https://brainly.com/question/30098276

#SPJ11

Bayes' rule, also known as Bayes' theorem or Bayes' law, is a mathematical formula used in probability theory and statistics. It provides a way to update our belief or probability of an event occurring, given new evidence.

The formula for Bayes' rule is:

P(A|B) = (P(B|A) * P(A)) / P(B)

where P(A|B) is the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, P(A) is the prior probability of event A occurring, and P(B) is the prior probability of event B occurring.

An example of how Bayes' rule can be used is in medical diagnosis.

Let's say a patient has a positive test result for a certain disease.

The probability of having the disease (event A) can be calculated using Bayes' rule, taking into account the sensitivity and specificity of the test.

The sensitivity is the probability of a positive test result given that the patient has the disease, and the specificity is the probability of a negative test result given that the patient does not have the disease.

By applying Bayes' rule, we can update the probability of having the disease based on the test result and the sensitivity and specificity values.

In short, Bayes' rule is a useful tool for updating probabilities based on new evidence. It is commonly used in various fields, including medicine, finance, and machine learning.

To know more about mathematical , visit ;

https://brainly.in/question/33520724

#SPJ11

Answer:

degree of the polynomial = 7

Number of terms = 2

Name = binomial

leading coefficient = 5

Step-by-step explanation:

The polynomial is x³y² - 5x³yz³

The degree of a polynomial is the highest exponent of any of its variables.

But in this case where we have two variable together, we sum up their exponents and the Hughes one will be the degree of the polynomial.

Thus;

x³y² has a degree of 3 + 2 = 5

5x³yz³ has a degree of 3 + 1 + 3 = 7

Thus,7 is the highest and the degree of the polynomial is 7.

There are two terms which are x³y² and 5x³yz³

Since it has two terms, it is a binomial.

To get the coefficient, I will rearrange in descending order of degree;

-5x³yz³ + x³y²

Thus, leading coefficient = 5

Answer:

y = 15

x = 43

Step-by-step explanation:

x + y = 48

x - 2y = 3

3y = 45

y = 15

x + y = 48

x + 15 = 48

x = 43

The required probability that 2 or fewer students are left-handed in a random sample of 65 students from the school is 0.0360.

Let X be a random variable which denotes the number of students who are left handed out of a sample of 65 students.

Here we have 65 students, therefore the number of trials would be 65. It would be reasonable to assume that the probability of one student being left handed is independent of any other student.

Therefore, the trials are independent.

There are only two possible outcomes for each trial i.e, either success or failure. The probability of success for each trial is 0.1

Hence we can say that X follows a binomial distribution with n = 65 and p = 0.1

X ~ Bin(65,0.1)

We need the probability that 2 or fewer students are left handed. This is given as :

P(X≤2)

we shall use the BINOM.DIST() function to find this

The syntax is given as:

= BINOM.DIST(number_s,trials,probability_s,cumulative)

Here,

number_s denotes the number of success required (2 in this case)

trials is the number of trials(65 in this case)

Probability_s is the probability of success in each trial (0.1 in this case)

cumulative, if true indicates the CDF or false if the PDF of X(TRUE in this case)

Hence the function which we use is

= BINOM.DIST(2,64,0.1,TRUE)

on running this code in any cell of excel, we get the probability as 0.035973

The required probability is 0.0360

Learn more about Probability here:

https://brainly.com/question/25688842

#SPJ4

A particular solution to the differential equation y" + 2y' + 2y = 5 sin t + 5 cos t is y = 5t sin t + 5t cos t.

To find a particular solution to the given differential equation, we can combine the particular solutions of the individual equations y' + 2y' + 2y = 5 sin t and y" + 2y' + 2y = 5 cos t.

Given:

y' + 2y' + 2y = 5 sin t    -- (Equation 1)

y" + 2y' + 2y = 5 cos t    -- (Equation 2)

we can add Equation 1 and Equation 2:

(Equation 1) + (Equation 2):

(y' + 2y' + 2y) + (y" + 2y' + 2y) = 5 sin t + 5 cos t

Rearranging the terms:

y" + 3y' + 4y = 5 sin t + 5 cos t   -- (Equation 3)

Now, we need to find a particular solution for Equation 3. We can start by assuming a particular solution of the form:

y = At(B sin t + C cos t)

Differentiating y with respect to t:

y' = A(B cos t - C sin t)

y" = -A(B sin t + C cos t)

Substituting these derivatives into Equation 3:

(-A(B sin t + C cos t)) + 3A(B cos t - C sin t) + 4At(B sin t + C cos t) = 5 sin t + 5 cos t

Simplifying the equation:

-AB sin t - AC cos t + 3AB cos t - 3AC sin t + 4AB sin t + 4AC cos t = 5 sin t + 5 cos t

Combining like terms:

(3AB + 4AC - AB)sin t + (4AC - 3AC - AC)cos t = 5 sin t + 5 cos t

Equating the coefficients of sin t and cos t on both sides:

2AB sin t + AC cos t = 5 sin t + 5 cos t

Matching the coefficients:

2AB = 5   -- (Equation 4)

AC = 5    -- (Equation 5)

Solving Equation 4 and Equation 5 simultaneously:

From Equation 4, we get: AB = 5/2

From Equation 5, we get: C = 5/A

Substituting AB = 5/2 into Equation 5:

5/A = 5/2

Simplifying:

2 = A

Therefore, A = 2.

Substituting A = 2 into Equation 5:

C = 5/2

So, C = 5/2.

Thus, the particular solution to y" + 2y' + 2y = 5 sin t + 5 cos t is:

y = 2t((5/2)sin t + (5/2)cos t)

Simplifying further:

y = 5tsin t + 5tcos t

Hence, the particular solution to y" + 2y' + 2y = 5 sin t + 5 cos t is y = 5tsin t + 5tcos t.

This particular solution satisfies the given differential equation and corresponds to the sum of the individual particular solutions. By substituting this solution into the original equation, we can verify that it satisfies the equation for the given values of sin t and cos t.

Learn more about particular solution

brainly.com/question/31591549

#SPJ11

Answer:

Scott always has 2 more fish per hour or S=M+2

Step-by-step explanation:

5-3 = 2, 9-7 = 2,...

For any given hour, Scott has reeled in 2 more fish compared to Megan.

We can see this by subtracting Scott's amount and Megan's amount for any row.

Because any given row has the same difference, this tells us that the slopes of each are the same.

The equation for Megan is y = 4x-1 while Scott's equation is y = 4x+1

x = number of hours, y = number of fish caught

Lines with equal slopes indicate parallel lines. If these trends keep up, then Megan will never catch Scott (she'll always be 2 fish behind him).

Another technique for defining the scope and range of functions is to utilize graphs.

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range. Following the insertion of an x value, the function outputs this sequence of values.

Graphs can be used as a second method to define the domain and range of functions. A graph's domain is the entire set of input values represented on the x-axis because the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.

The set of all possible inputs and outputs is known as a function's domain, and the same is true for its range. It is crucial to consider a function's domain and range. The range contains all of the function's output values, while the domain contains all of the real numbers that can be used as input values.

To learn more about domain and range refer to:

https://brainly.com/question/11736212

#SPJ1

Hey there!

xy/z

x = -2

y = -3

z = 4

Substitute the values of x, y & z in the equation.

xy/z

= (-2)×(-3)/4

= 6/4

= 3/2

Hope it helps ya!

Answer:

Im not smart sorry

Step-by-step explanation:

If y follows a chi-squared distribution with v = 10, then its expected value and variance are given by: E(y) = v = 10, Var(y) = 2v = 20. The probability that X^2 exceeds 6.737 is approximately 0.4238.

Now, let X = √y. Then X follows a chi distribution with v = 10 degrees of freedom. We have:

E(X) = E(√y) = √E(y) = √10

Var(X) = Var(√y) = 1/4 Var(y) = 5

To find P(X^2 > 6.737), we can use the definition of the chi-squared distribution. We have:

P(X^2 > 6.737) = P(X > √6.737) + P(X < -√6.737)

The chi distribution is symmetric, so P(X < -√6.737) = P(X > √6.737). Therefore,

P(X^2 > 6.737) = 2P(X > √6.737)

We can standardize X by subtracting its mean and dividing by its standard deviation:

Z = (X - √10) / √5

Then,

P(X > √6.737) = P(Z > (√6.737 - √10) / √5)

Using a standard normal table or calculator, we find that:

P(Z > 0.798) = 0.2119

Therefore,

P(X^2 > 6.737) = 2P(X > √6.737) = 2(0.2119) = 0.4238

So the probability that X^2 exceeds 6.737 is approximately 0.4238.

Learn more about probability at: brainly.com/question/30034780

#SPJ11

Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The perpendicular line bisect the base of isosceles triangle.

Then,

9^2=y^2-x^2

81=324-243

81=81

So the correct answer is D

I Hope this will be helpful for you

we can conclude that the end behavior of f(x) is that as x approaches positive or negative infinity, f(x) approaches infinity.

From the given graph, we can see that as x approaches infinity (i.e., as x → ∞), f(x) also approaches infinity (i.e., f(x) → ∞). Similarly, as x approaches negative infinity (i.e., as x → -∞), f(x) also approaches negative infinity (i.e., f(x) → -∞).

The end behavior of a function describes the behavior of the function as the input variable (in this case, x) approaches positive or negative infinity. It tells us what happens to the function values (in this case, f(x)) as x becomes very large in magnitude, either positively or negatively.

we can see that as x moves towards positive infinity (i.e., as x → ∞), the curve of the function moves upward without bound. This means that the value of f(x) increases without limit as x increases without limit. Similarly, as x moves towards negative infinity (i.e., as x → -∞), the curve of the function moves downward without bound. This means that the value of f(x) decreases without limit as x decreases without limit.

Therefore, we can conclude that the end behavior of f(x) is that as x approaches positive or negative infinity, f(x) approaches infinity.

Learn more about infinity from

https://brainly.com/question/30340151

#SPJ11

-1/7, since parallel lines have equal slopes.

The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.

The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.

Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.

You can leanr more about insurance at

https://brainly.com/question/29677494

#SPJ4

The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

for such more questions on factors

https://brainly.com/question/25829061

#SPJ8

Answer:

12,853.85568

Step-by-step explanation:

\(A=P(1+\frac{r}{n})^{nt}\)

A= final amount

P= inital principal balance

r= interest rate

n= number of times interest applied per time period

t= numbers of period

\(A=3,686(1+\frac{.07}{4})^{(4)(18)}\)

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

For more questions on probability

https://brainly.com/question/25839839

#SPJ8

Answer:

62 to 1

Step-by-step explanation:

434÷7=62

so yeah