A dog is leashed to a point in the center of a large yard, so the area the dog is able to explore is circular. the leash is 15 feet long. what is the area of the region the dog is able to explore? round to the nearest tenth.

The variance of S, the sum of the outcome of a six-sided die and three times the outcome of a four-sided die, is 10.5. The probability distribution of S ranges from 4 to 18, with probabilities of 1/24, 1/12, 1/6, 1/6, 1/6, 1/6, 1/12, 1/12, 1/12, 1/24, 1/24, 1/24, 1/24, 1/24, 1/24, and 1/24 respectively. The expected value of S is 10, and the approximate value of E[S] is also 10. The expected value of the expression \((X1+3Y1-2Y2)^2\), where Y2 is the outcome of a second four-sided die, is 52.33.

1. To calculate the variance of S, we first need to find the variances of X1 and Y1, which are (1/6)\((6-1)^2\) = 5/6 and (1/4)\((4-1)^2\) = 3/4 respectively. Since X1 and Y1 are independent, the variance of their sum S is the sum of their variances, resulting in 5(5/6) + 3(3/4) = 6.417.

2.To determine the probability distribution of S, we consider all possible outcomes. The possible values of S range from 4 to 18, and the probabilities are calculated by considering all combinations of the six-sided die and four-sided die rolls. The probabilities are as follows: 1/24 for S = 4, 1/12 for S = 5 or 6, 1/6 for S = 7, 1/6 for S = 8, 1/6 for S = 9, 1/6 for S = 10, 1/12 for S = 11 or 12, 1/12 for S = 13 or 14, 1/12 for S = 15 or 16, and 1/24 for S = 17 or 18.

3.The expected value of S, E[S], is calculated by summing the products of each possible outcome and its corresponding probability. Since we have the probabilities from the previous step, we multiply each outcome by its probability and sum them up. E[S] = 4(1/24) + 5(1/12) + 6(1/12) + 7(1/6) + 8(1/6) + 9(1/6) + 10(1/6) + 11(1/12) + 12(1/12) + 13(1/24) + 14(1/24) + 15(1/12) + 16(1/12) + 17(1/24) + 18(1/24) = 10.

4.The approximate value of E[S] is also 10, as calculated in the previous step.

5.To find the expected value of \((X1+3Y1-2Y2)^2\), we first calculate the expected value of \(X1^2\), which is (1/6)\((1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2)\) = 91/6. Similarly, the expected value of \(Y1^2\) is (1/4)\((1^2 + 2^2 + 3^2 + 4^2)\) = 30/4 = 15/2. Since Y1 and Y2 are independent, the expected value of \(Y2^2\) is the same as \(Y1^2\). Finally, we calculate the expected value of \((X1+3Y1-2Y2)^2\) by substituting the expected values we found into the expression, resulting in (91/6) + 3(15/2) + 2(15/2) = 52.33.

Learn more about variance here:

https://brainly.com/question/31698743

#SPJ11

Answer:

4 and 6?

im not sure if you meant numbers

Step-by-step explanation:

The snail will take approximately 0.43 hours or 25.8 minutes to travel 12 feet at the speed of 8.5 meters per hour.

Given, A snail moves at a speed of 8.5 meters per hour, 1m = 3.28ft. Let's convert meters per hour into feet per hour by multiplying it with 3.28ft/m. So, 8.5 meters per hour = 8.5 × 3.28 feet per hour ≈ 27.88 feet per hour.

Now, to calculate the time taken by a snail to travel 12 feet, we can use the formula: Time = Distance ÷ Speed

Time taken = 12 feet ÷ 27.88 feet per hour ≈ 0.43 hours (rounded to two decimal places)

Now, let's convert 0.43 hours to minutes by multiplying it with 60 minutes per hour: 0.43 hours × 60 minutes per hour ≈ 25.8 minutes (rounded to one decimal place). Therefore, it will take approximately 0.43 hours or 25.8 minutes for the snail to travel 12 feet at the speed of 8.5 meters per hour.

To know more about speed refer here:

https://brainly.com/question/31052185#

#SPJ11

Answer:

V≈6.93

Step-by-step explanation:

AB=s(s﹣a)(s﹣b)(s﹣c)

V=ABh

s=a+b+c

2

Solving forV

V=1

4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1

4·4·﹣24+2·(2·2)2+2·(2·2)2﹣24+2·(2·2)2﹣24≈6.9282

Answer:

x°= 34°

m<x and angle measuring 34° are corresponding angles since two lines are parallel with a third line intersecting them.

Answer:

5

Step-by-step explanation:

number of chocolate chip cookies = 36 × ¼ = 9

number of oatmeal cookies = 36 × ⅓ = 12

36 - 9 - 12 = 15

Alex made 15 peanut butter cookies.

Answer:

Both are equivalent: 10/16 and 40/64

Step-by-step explanation:

I hope this helps you :)

The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

To know more about Triangle visit:

brainly.com/question/2773823

#SPJ4

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

Know more about level of significance here:

https://brainly.com/question/30542688

#SPJ11

Answer:

75 Pages

Step-by-step explanation:

If he has 40% completed, it is 0.40 as a decimal.  We are trying to solve for the total number of pages in the book, or the whole.

part/whole = percent  

Let x = total number of pages in the book

30/x=0.40

x=30/0.40 = 75 pages in the book

Answer:

1.121

Step-by-step explanation:

We can align them:

0.001

1 .010

0.1 10

Then we can add each horizontal line.

We get, 1.121

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

To know more about Net present value   visit

https://brainly.com/question/32720837

#SPJ11

The most picked number between 1 and 10 is statistically 7.

"Most picked number" generally refers to the number that is most frequently chosen or selected.

It is difficult to determine the value in general without any specific context or situation.

However, statistically speaking, the number 7 is often considered the most popular choice. This is because it is considered a lucky number in many cultures and is also a common choice for people who do not have a specific number in mind.

Nevertheless, it's important to note that this may not always be the case and can vary depending on the context or situation as the probability of picking each number is equally likely (0.1).

Learn more about most picked number from the below link:

https://brainly.com/question/30763377

#SPJ4

Answer:

The third one!

Step-by-step explanation: 5 5 5 5 its 5!

15%

Step-by-step explanation:

Absent= 6

Total student = 40

\( \frac{6}{40} \times 100 \\ \\ \frac{600}{40} = 15\%\)

Step-by-step explanation:

Hey there!!

We can simply do it.

Here,

Total students =40

Absent students = 6

Now,

\(absent\% = \frac{no.asent}{total \: student} \times 100\%\)

Keep all values.

\(absent\% = \frac{6}{40} \times 100\%\)

= 15%

Therefore, the absent percentage is 15%.

Hopeit helps...

Answer:

$68000

Step-by-step explanation:

Answer:

$6800

Step-by-step explanation:

30x1600+10x2000

=48000+2000

=68000

When Solver is unable to find a solution to a problem, it can be an indication of various issues. One possible cause is that the problem may be too complex for Solver to solve within the given constraints.

In such cases, it may be necessary to adjust the problem parameters or seek alternative solutions. Another possible cause of Solver's inability to find a solution could be due to incorrect input data. This can lead to inconsistent or contradictory constraints, making it impossible for Solver to arrive at a feasible solution. Lastly, Solver may fail to find a solution due to numerical errors or limitations in the algorithm used. These issues can arise when dealing with large datasets or highly non-linear problems. In any case, when Solver is unable to find a solution, it is important to carefully examine the problem and its parameters, and consider alternative approaches. Sometimes, a small adjustment to the input data or constraints can make all the difference in arriving at a successful solution.  In such cases, Solver may struggle to find an accurate or optimal solution. Ill-conditioned problems typically involve numerical instability or poor scaling, while infeasible problems occur when the given constraints cannot be satisfied simultaneously. It is crucial to analyze and refine the problem to enable Solver to find a viable solution effectively. When there is a problem with Solver being unable to find a solution, it often indicates the presence of a(n) ill-conditioned or infeasible problem.

Learn more about constraints here

https://brainly.com/question/30591474

#SPJ11

Answer:

Close, but the answer is 1/2

Step-by-step explanation:

The answer would be 2 when you are finding the scale factor of ABCD to EFGH, but since it is going from EFGH to ABCD, then all you have to do is divide by 2 or multiply by 1/2.

EFGH to ABCD= 12 • 1/2 = 6 or 12 ÷ 2 = 6

When the input x is -18, the output h is 14. The answer is obtained using substitution method.

What is substitution method?

One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Now, we are given h = 17+x/6

So, when the input x is -18, using substitution method,

h=17+(-18/6)

=17+(-3)

=17-3

=14

Hence, when the input x is -18, the output h is 14.

Learn more about substitution method from the given link

https://brainly.com/question/30095039

#SPJ1

Answer:

k = 7

Step-by-step explanation:

Applying,

S = (y₂-y₁)/(x₂-x₁)................ Equation 1

Where S = slope of the line.

From the question,

Given: y₂ = 10, y₁ = 4, x₂ = k, x₁ = 1, S = 1

Substitute these values into equation 1

1 = (10-4)/(k-1)

crossmultiplying,

(k-1) = (10-4)

k-1 = 6

k = 6+1

k = 7

The material remained for the blanket after trimming off by Keith is 2.5 yards.

Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6

Performing multiplication and division on Right Hand Side of the equation

Trimmed material = 1/2 or 0.5

Now, we need to subtract the trimmed material from overall amount of material

Remaining material = 3 - 0.5

Performing subtraction on Right Hand Side of the equation

Remaining material = 2.5 yards

Hence, 2.5 yards of material remained.

Learn more about multiplication -

https://brainly.com/question/10873737

#SPJ4

Answer:

2

Step-by-step explanation:

First you add 4 to both sides and get

2x=4

then you divide by 2 and get

4/2=x

4/2=2

x=2

Answer:

+2 or -2

Step-by-step explanation:

move 4 after equal sign

now it's x² =4 and put a root on the two parts of equation and this is what you get

The expression (-9+i)-(12-5i) can be represented to -21+6i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example:

2 + 5i , then:

2 real part

5i imaginary part

About operations, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 9i² = 9*(-1)=-9.

When you sum or subtract complex numbers, you can only sum or subtract: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. See examples:

(2 + 5i) + (2 + 5i) = 4+10i

(4 + 10i) - (2 + 5i) = 2+5i

Therefore, the result for the (-9+i)-(12-5i) will be:

-9+i-12+5i= -21+6i

Read more about the complex number here:

https://brainly.com/question/5564133

#SPJ1

Answer:

(0, 2)

Step-by-step explanation:

The y-intercept on a graph represents the point where the graph intersects the y-axis. In the equation y = x + 2, the y-intercept can be found by setting x = 0 and solving for y.

When x = 0:

y = 0 + 2

y = 2

Therefore, the y-intercept on the graph of the function y = x + 2 is (0, 2).

The cosine similarity between vectors x = (7, 14) and y = (11, 3) is approximately 0.68 when rounded to two decimal places.

To compute the cosine similarity, we follow these steps:

Calculate the dot product of the two vectors: x · y = (7 * 11) + (14 * 3) = 77 + 42 = 119.

Compute the magnitude of vector x: ||x|| = sqrt((7^2) + (14^2)) = sqrt(49 + 196) = sqrt(245) ≈ 15.65.

Compute the magnitude of vector y: ||y|| = sqrt((11^2) + (3^2)) = sqrt(121 + 9) = sqrt(130) ≈ 11.40.

Multiply the magnitudes of the vectors: ||x|| * ||y|| = 15.65 * 11.40 ≈ 178.71.

Divide the dot product of the vectors by the product of their magnitudes: cosine similarity = x · y / (||x|| * ||y||) = 119 / 178.71 ≈ 0.6668.

Rounding this value to two decimal places, we get a cosine similarity of approximately 0.68.

To learn more about dot product click here:

brainly.com/question/23477017

#SPJ11

The cosine similarity between vectors x = (7, 14) and y = (11, 3) is approximately 0.68 when rounded to two decimal places.

To compute the cosine similarity, we follow these steps:

Calculate the dot product of the two vectors: x · y = (7 * 11) + (14 * 3) = 77 + 42 = 119.

Compute the magnitude of vector x: ||x|| = sqrt((7^2) + (14^2)) = sqrt(49 + 196) = sqrt(245) ≈ 15.65.

Compute the magnitude of vector y: ||y|| = sqrt((11^2) + (3^2)) = sqrt(121 + 9) = sqrt(130) ≈ 11.40.

Multiply the magnitudes of the vectors: ||x|| * ||y|| = 15.65 * 11.40 ≈ 178.71.

Divide the dot product of the vectors by the product of their magnitudes: cosine similarity = x · y / (||x|| * ||y||) = 119 / 178.71 ≈ 0.6668.

Rounding this value to two decimal places, we get a cosine similarity of approximately 0.68.

To learn more about dot product click here:

brainly.com/question/23477017

#SPJ11

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

Learn more about exponential function here:

https://brainly.com/question/14355665

#SPJ1

Answer:

The correct answer is D. 3x² - x + 3

Step-by-step explanation:

4x² - x + 6 - (x² + 3)

= 4x² - x² - x + 6 - 3

= 3x² - x + 3

Answer:

3/4x-2

Step-by-step explanation:

3−4=8

∴3=4+8

∴4=3−8

∴=14(3−8)=34−2

Answer + Step By Step: