Solve the problem. Points: 7 74) Suppose a point P is on a circle whose center is O with radius 25 meters. A ray OP is rotating with the angular speed (a) Find the angle generated by P in 5 seconds. (

The joint PDF of X and Y is fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

The joint probability density function (PDF) of X and Y can be obtained by multiplying the individual PDFs of X and Y, as they are independent random variables.

Given:

X ~ Exponential(λ), with mean 1 (λ = 1)

Y ~ Uniform(0, X), for 0 < y < x

To find the joint PDF, we first need to express the PDFs of X and Y.

PDF of X:

fX(x) = λ * exp(-λx) for x > 0 (Exponential distribution with parameter λ)

PDF of Y:

fY(y|x) = 1 / x for 0 < y < x (Uniform distribution on interval [0, x])

Now, we can find the joint PDF by multiplying these individual PDFs:

fx.x (x, y) = fX(x) * fY(y|x)

Substituting the PDFs:

fx.x (x, y) = (λ * exp(-λx)) * (1 / x)

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x

Therefore, the fully specified joint PDF of X and Y is:

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

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Step-by-stepAnswer:

∠4 and ∠5

Step-by-step explanation:

Both angels seem to add up to 180°

Answer:

option 2

Step-by-step explanation:

The only kinds of lines with undefined slopes are vertical lines.

Answer:

The second graph.

Step-by-step explanation:

A vertical line has undefined slope so it is the second graph.

If 6 square feet weighs half a pound, the 10 square feet weigh is 5/6 pounds.

The weight of a certain material varies directly with the surface area of that material.

So if surface area is A and weight of a certain material is w.

Then A ∝ w

After removing the varies the constant k is added.

A = kw

From the question A = 6 and w = 1/2 pounds.

So 6 = k × 1/2

Multiply by 2 on both side we get

k = 12

Since A = 10

So 10 = 12 × w

Divide by 12 on both side, we get

w = 10/12

On simplifying

w = 5/6 pounds

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Answer:

Hope this helps!

23 is a prime number, so therefore the factors of it is just 1 and itself (23)

Answer:

£121

Step-by-step explanation:

5/12 of the total coins = 5/12 x 96 = 40   ⇒   40 coins are £2 coins

26 of the coins are £1 coins

Number of 50p coins = 96 - 40 - 26 = 30  ⇒  30 of the coins are 50p coins

Total money collected = 40 x £2 + 26 x £1 + 30 x £0.50 = £121

(rememberinf to convert 50p into £s)

Answer:

\(x=\displaystyle\frac{3\pm\sqrt{569}}{4}\)

Step-by-step explanation:

Hi there!

\(f(x) = -2x(x+7)+10x+70\\f(x) = -2x^2-7x+10x+70\\f(x) = -2x^2+3x+70\)

We can solve this by using the quadratic formula, which states:

\(x=\displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) where \(f(x)=ax^2+bx+c\)

Plug in the values a, b and c:

\(x=\displaystyle\frac{-3\pm\sqrt{3^2-4(-2)(70)}}{2(-2)}\\\\x=\displaystyle\frac{-3\pm\sqrt{9+560}}{-4}\\\\x=\displaystyle\frac{-3\pm\sqrt{569}}{-4}\\\\x=\displaystyle\frac{3\pm\sqrt{569}}{4}\)

I hope this helps!

The length of the base of the rectangle is B = 11 yards  

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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The equation to represent Sand supply of contact lens pairs, y, after x months is 5 + 1.5x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Here, Sandy wears contact lenses. She starts the year with 5 pairs of lenses, and she uses 3 pairs of contacts every 2 months.

The equation to represent Sand supply of contact lens pairs, y, after x months so be:

5 + (3/2 × x)

5 + 1.5x

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We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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Answer:

Slope-intercept: y=3/4x+1

Sorry idk how to do general form

Step-by-step explanation:

Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.

The slope of this graph is 3/4, and the y-intercept is 1.

Answer:

Slope-intercept form: \(y=\frac{3}{4}x+1\)

General form: \(-3/4x+y-1\)

Step-by-step explanation:

Firstly, to get the slope intercept form, we need to find the slope and the y-intercept.  To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is \(\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}\). So, after we plug in those values we get in the two points, we can see that \(\frac{4-1}{4-0}\), so the slope is \(\frac{3}{4}\). The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, \(mx+b\), where m is the slope and b is the y-intercept, m is \(\frac{3}{4}\) and b is 1. So, our final answer for the slope-intercept form is \(y=\frac{3}{4}x+1\). Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, \(y=\frac{3}{4}x+1\), we can subtract y from both sides to get 0 on the left, like this: \(0=\frac{3}{4}x+1-y\). Then, we can rearrange the variables to general form: \(0=\frac{3}{4}x-y+1\\\). That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!

Answer:

26r^2 + 36r.

Step-by-step explanation:

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer:

y+9=-2(x-9)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(13-(-9))/(-2-9)

m=(13+9)/-11

m=22/-11

simplify

m=-2

y-y1=m(x-x1)

y-(-9)=-2(x-9)

y+9=-2(x-9)

Answer:

Can I see an attachment if there is a graph or something???

Answer:

1 is the answer to this question

The missing number in the table is 1296

The y-values of the table form a geometric sequence as shown:

6, 36, 216,......

The nth term of a geometric progression is expressed using the formula;

\(T_n=ar^{n-1}\)

Substitute the given parameters into the formula:

\(T_5=6(6)^{4-1}\\T_5=6(6)^3\\T_5=1296\)

Hence the missing number in the table is 1296

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Answer:

1296

Step-by-step explanation:

Pie charts usually show the components or categories of a whole.

A pie chart is a circular graphical representation used to display categorical data. It divides the circle into sectors, where each sector represents a specific category or component.

The size of each sector or "slice" is proportional to the relative frequency or proportion of the category it represents. The whole circle represents the total or 100% of the data being summarized.

Pie charts are good for summarizing categorical data and visually representing the distribution or composition of different categories within a dataset.

They provide a clear visual depiction of the proportions and relative sizes of the categories. Pie charts are especially useful when you want to emphasize the comparisons between different categories or show the relationship between parts and the whole.

However, there are cases where pie charts are not useful or may not be the most appropriate choice. For instance:

1. When there are too many categories: Pie charts become less effective when there are numerous categories, as the slices can become too small and difficult to interpret.

2. When the data is continuous or numerical: Pie charts are primarily used for categorical data, and other types of charts like bar charts or line graphs are more suitable for representing continuous or numerical data.

3. When precise comparisons or exact values are necessary: Pie charts provide a visual overview of proportions but do not accurately convey precise numerical values. In such cases, using a table or other types of charts may be more appropriate.

4. When the data has overlapping or similar proportions: Pie charts can be misleading if the categories have similar proportions, as it becomes challenging to differentiate between the slices.

It is important to consider the specific context and data characteristics to determine whether a pie chart is the most effective and informative visualization choice.

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Step-by-step explanation:

√(20+5²)=√{20+25}=√45=3√5

A group of student organization who wants to study about voting preferences in its students during presidential election in 2012. So, they selected a sample of 120, is an example of stratified random sampling.

Stratified random sampling is a widely used statistical technique in which a population is divided into different subgroups, or strata, based on some shared characteristics. The purpose of stratification is to ensure that each stratum in the sample and to make inferences about specific population subgroups, that is they share (e.g., race, gender, educational attainment).

Therefore, the stratified random sample involves dividing the population into two or more strata (groups). These strata are expressed as H. A stratified random sampling because a random sample has been taken from each different strata (Freshmen through seniors).

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Answer: 8/7

Step-by-step explanation:

Answer:

None of the above

Step-by-step explanation:

Measure of one base angle: 52°

Measure of the other base angle: 52°

Measure of the third angle: x

Sum of the measures of the three angles: 180°

Equation:

x + 52 + 52 = 180

x + 104 = 180

Answer: None of the above

To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:

1. Start with the initial B&B tree, where the root node represents the original problem.

2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for

\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)

3. At each node, perform the following steps:

  - Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.

  - If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.

  - If the LP solution is integer, update the current best solution if the objective value is higher.

  - If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.

4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.

5. The node with the highest objective value among the integer feasible solutions is the optimal solution.

6. Optionally, backtrace through the tree to retrieve the optimal solution variables.

Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.

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Answer:

Step-by-step explanation:

AT first, draw the reference line, which are given. If I take PQ as base, I won't need to draw PQ line as reference.

I took PQ(5.5cm) as base. Then, take 4.8cm in your compass by centering at point Q. Draw an arc. Then take 4.2 cm in your compass from the reference line which you have drawn and then centre at point P and draw an arc. Both the arcs will meet at one point. Then join the lines to form the Triangle PQR

The probability that a student who did not complete the homework passed the test is 0.25.

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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Answer:

c

Step-by-step explanation:

Given:

Required:

We need to find the volume of given cone

Explanation:

Take

The volume of cone is

Plug the values

Final answer:

Volume of cone is 84.78 cubic cm