Find the length of the third side. If necessary, write in simplest radical form.

The length of side a is 50 if the angle ∠bac is 50° and the length of side b is 20 and side c is 35 using cosine law.

Length of side b = 20

Length of side c = 35

Angle ∠bac =  50°

To calculate the length of the side a, we need to use the cosine law. The formula is:

\(a^2 = b^2 + c^2 - 2bc cos(A)\)

Substituting the given values in the formula, we get:

\(a^2 = 20^2 + 35^2 - 2(20)(35)cos(50°)\)

\(a^{2}\) = 400 + 1225 + (1400)*(0.642)

\(a^{2}\) = 1625 + 898.8

a = \(\sqrt{2523.8}\)

a = 50

Therefore we can conclude that the length of side a is 50 using cosine law.

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The real part of the complex number is -5 and the imaginary part is -7i

From the question, we have the following parameters that can be used in our computation:

Complex number = -7i - 5

For a complex number represented as

a + bi

We have

Real = a

Imaginary = bi

using the above as a guide, we have the following:

Real = -5

Imaginary = -7i

Hence, the real part is -5 and the imaginary part is -7i

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One possible explanation for the difference in responses to the survey question could be the order in which the questions were presented. It is possible that the question that was answered yes by 75% of one group was presented earlier in the survey for that group, while it was presented later in the survey for the other group.

Research has shown that the order in which questions are presented can have an effect on how people respond to them. This effect is known as "question order bias" or "primacy and recency effects". The first few questions of a survey can set the tone for how participants answer subsequent questions, and the order of the questions can affect the responses.

Another possible explanation for the difference in responses could be sampling error or chance. Even if the two groups are similar, there can still be variability in the responses due to random chance. If the survey question was a sensitive topic or there was ambiguity in the wording of the question, this could also contribute to the difference in responses.

In summary, the difference in responses to the survey question between the two groups could be due to question order bias, sampling error, or other factors. It is difficult to determine the exact cause without more information about the survey and the specific question that was asked.

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Answer:

Positive interval: x is in (-5, infty)

Negative interval: x is in (-infty, -5)

Step-by-step explanation:

A fraction is positive when the numerator and denominator have the same sign. Since the numerator is positive in this case, the fraction will be positive when it's denominator is also positive. Thus, we need to solve x+5>0. Subtracting 5 on both sides gives x>-5.

Positive interval: x is in (-5, infty)

A fraction is is negative when the numerator and denominator have the different signs. Since the numerator is positive in this case, the fraction will be negative when it's denominator is negative. Thus, we need to solve x+5<0. Subtracting 5 on both sides gives x<-5.

Negative interval: x is in (-infty, -5)

A fraction doesn't have an output when it's denominator is 0. That is, in this case when x+5=0 which is when x is -5.

a)  The random variable is the number of fish caught in a single cast of the line and and the parameter is the probability of hooking a fish with a single hook

b) The probability of catching 9 fish on a single cast of the line is:

P(X=9) = p^9

c) The probability of catching at least one fish on a single cast is

1 - (1-p)^9

d) The smallest value of n that satisfies this condition is:

n = ⌈log(1-p/100) / log(1-p)⌉

(a) The random variable is the number of fish caught in a single cast of the line, denoted by X. This is a discrete random variable, taking values from 0 to 9. The parameter is the probability of hooking a fish with a single hook, denoted by p.

(b) The probability of catching 9 fish on a single cast of the line is:

P(X=9) = p^9

This is because each hook has a probability of p of catching a fish, and since the events are independent, the probability of all 9 hooks catching a fish is simply the product of their individual probabilities.

(c) The probability of catching at least one fish on a single cast is:

P(X ≥ 1) = 1 - P(X=0)

= 1 - (1-p)^9

This is because the probability of not catching any fish is the complement of the probability of catching at least one fish.

(d) Let n be the number of hooks needed to catch at least one fish on each cast with probability p%. We need to find the smallest value of n that satisfies this condition. Using the complement rule, the probability of not catching a fish with n hooks is:

P(X = 0) = (1-p)^n

So the probability of catching at least one fish is:

P(X ≥ 1) = 1 - (1-p)^n

We want this probability to be at least p%, so we have:

1 - (1-p)^n ≥ p/100

Simplifying, we get:

(1-p)^n ≤ 1 - p/100

Taking the logarithm of both sides, we get:

n log(1-p) ≤ log(1-p/100)

Dividing by log(1-p), we get:

n ≥ log(1-p/100) / log(1-p)

So the smallest value of n that satisfies this condition is:

n = ⌈log(1-p/100) / log(1-p)⌉, where ⌈x⌉ denotes the smallest integer greater than or equal to x.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

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Larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

For a population that is not normally distributed, the distribution of the sample means will approach a normal distribution as the size of the sample increases.

This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means becomes more normal regardless of the shape of the population distribution.

Therefore, larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

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The estimated mean amount of money spent per household on internet service each month is $59.95 with confidence interval.

To calculate the estimated mean amount of money spent per household on internet service each month, we first need to find the lower and upper bounds of the confidence interval. The lower bound is $47.45 and the upper bound is $72.45. We then take the average of these two numbers to get the estimated mean. The average of $47.45 and $72.45 is

($47.45 + $72.45) / 2

= $59.95.

Therefore, the estimated mean amount of money spent per household on internet service each month is $59.95.

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The probability for the given condition is, 0.56.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession.

We have to find the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.

P(white ball) = 14 / (11 + 14) = 14 / 25

P(2nd ball is white) = P(first ball is white)*P(2nd ball is white) + P(first ball is black)*P(2nd ball is white)

= (14 / 25) * (13 / 24) + (11 / 25) * (14 / 24)

=0.56

Hence, the probability for the given condition is, 0.56.

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The target population is the population of interest that researchers aim to generalize their findings to.

The correct answer is c. sample.

In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.

The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.

An element refers to a single member of the population or sample.

The target population is the population of interest that researchers aim to generalize their findings to.

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Answer:

counted down

Step-by-step explanation:

it was counting up and went down by couting down in 2

Answer:

Step-by-step explanation:

There are 19 - 5 = 14 students between the number 5 and 19, either side, so the total number is:

Answer:

11.18 or 11 yards

Step-by-step explanation:

15² - 10² = x²

225 - 100 = x

225 - 100 = 125

√125 = 11.180339887498948482045868343656

11.180339887498948482045868343656 rounded to the nearest hundredth is 11.18; to the nearest tenth is 11.2; and to the nearest one is 11.

The value of a is 10 by solving the quadratic equation by completing the square method.

In this question,

Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. It is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)^2 + k.

The quadratic equation is

10x^2 + 40x - 13 = 0

Solving the quadratic equation by completing the square as

Step 1:

10x^2 + 40x = 13

Step 2:

10(x^2 + 4x) = 13

Thus on comparing the step 2 with the equation a(x^2 + 4x) = 13, the value of a is 10.

Hence we can conclude that the value of a is 10 by solving the quadratic equation by completing the square method.

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The measure of the obtuse angle in the triangle is 108 degrees.

A triangle is a polygon with three sides. The total sum of the angles in a triangle is 180 degrees.

Therefore, the measure of the obtuse angle in the triangle can be found as follows;

An obtuse angle is an angle which is greater than 90° and less than 180°.

Hence, the angles of the triangle are 1x, 3x and 6x.

3x + 1x + 6x = 180

10x = 180

x = 180 / 10

x = 18

Therefore, the obtuse angle of the triangle is 6(18) = 108 degrees.

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Answer:

c) 108 on edgen

The equation of the surface of revolution generated by revolving x = (1/z)^z about the z-axis is x = e^(-y).

To find the equation of the surface of revolution, we start with the parametric equation x = (1/z)^z, y = t, z = t. We eliminate the parameter t by substituting z for t in the equation x = (1/z)^z. Simplifying further, we obtain x = e^(-y).

This equation represents the surface of revolution generated by revolving the curve x = (1/z)^z about the z-axis. The exponentiation by e^(-y) signifies that the x-coordinate changes exponentially as the y-coordinate varies.

Therefore, as we revolve the curve around the z-axis, it forms a surface with an exponential decay in the x-direction. Hence, the equation x = e^(-y) describes the surface of revolution.

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Answer:

it's commutative property of addition

Step-by-step explanation:

commutative property is when we can change the position or swap the numbers when adding or multiplying any two numbers.

The Yankee bond is a Dollar-denominated debt securities issued by foreign corporations and traded in u.s. markets.

According to the statement

we have to find that the term and explain all about it which is a Dollar-denominated debt securities issued by foreign corporations and traded in u.s. markets.

So, For this purpose, we know that

We have given that the

The term is a dollar denominated debt and it is traded in the u.s. market.

From this information, we know that the

A Yankee bond is a debt obligation issued by a foreign entity, such as a government or company, which is traded in the United States and denominated in U.S. dollars.

Hence, It is called the Yankee bond.

So, The Yankee bond is a Dollar-denominated debt securities issued by foreign corporations and traded in u.s. markets.

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a) The stationary distribution for this random walk is π = (0, 0, 0, ..., 0). b) The random walk will never stay at state 0 in the long run.

(a) To find the stationary distribution for the simple symmetric random walk on [0,1,..,k) with reflecting boundaries, we need to determine the probabilities of being at each state in the long run.

Let's denote the stationary distribution as π = (π₀, π₁, ..., πₖ), where πᵢ represents the probability of being at state i.

In a stationary distribution, the probabilities must satisfy the following conditions:

The sum of probabilities is equal to 1: π₀ + π₁ + ... + πₖ = 1.

The probabilities at reflecting boundaries (states 0 and k) are zero: π₀ = πₖ = 0.

For the states between 1 and k-1, the stationary distribution probabilities can be determined by considering the balance equations. The balance equation states that the flow of probability into a state is equal to the flow of probability out of that state.

For the interior states (1 to k-1), the balance equations can be written as:

πᵢ-1 = 1/2 * πᵢ + 1/2 * πᵢ₊₁, for i = 1, 2, ..., k-1.

Using these equations, we can solve for the stationary distribution probabilities. We start with the balance equation for state 1:

π₀ = 1/2 * π₁ + 1/2 * π₀ (reflecting boundary at 0)

Since π₀ = 0 (reflecting boundary at 0), the equation becomes:

0 = 1/2 * π₁ + 0

π₁ = 0

Now we can proceed with the remaining balance equations:

π₀ = 1/2 * π₁ + 1/2 * π₂

0 = 1/2 * 0 + 1/2 * π₂

0 = π₂

Following this pattern, we see that πᵢ = 0 for all i from 1 to k-1.

Thus, the stationary distribution for this random walk is:

π = (0, 0, 0, ..., 0).

(b) Since the stationary distribution is zero for all states, including state 0, the random walk will never stay at state 0 in the long run. Therefore, the walk will never return to state 0 if it starts at state 0. The expected number of steps for the walk to return to 0 starting from state 0 is undefined or infinite.

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Answer:

3

Step-by-step explanation:

72/4=18 18-3=15 15/5=3

If 3 added to five times a number, and the result is multiplied by 4, the number that satisfies the given conditions is x = 3.

Let's break down the problem step by step to find the number.

First, we start with a variable to represent the unknown number. Let's call it "x".

The problem states that "3 added to five times a number," which can be expressed as 5x + 3.

Next, it says that "the result is multiplied by 4," so we can write the equation as 4(5x + 3).

Finally, the problem states that "the final result is 72," so we set the equation equal to 72:

4(5x + 3) = 72

To solve for x, we simplify the equation:

20x + 12 = 72

Next, we subtract 12 from both sides:

20x = 60

Finally, we divide both sides by 20:

x = 3

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Answer:

V=I R

120= I × 20

I = 120÷20

I = 6 A

................................

We can see that the experimental probability is smaller than the theoretical one.

The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:

T = 3/8 = 0.375

The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:

E = 12/40 = 0.3

So the experimental probability is smaller than the theoretical one.

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We are given a boundary value problem represented by the differential equation y" + 400π²y = 0, with the boundary conditions y(0) = 0 and y'(1) = 1. We need to determine whether this problem is homogeneous or nonhomogeneous and either solve the problem or show that it has no solution.

To determine whether the given boundary value problem is homogeneous or nonhomogeneous, we examine the differential equation y" + 400π²y = 0. A differential equation is considered homogeneous if all the terms involve the dependent variable and its derivatives, and there are no additional functions or constants involved.

In this case, the differential equation y" + 400π²y = 0 is indeed homogeneous because it only involves the dependent variable y and its derivatives. There are no additional functions or constants present.

To solve the boundary value problem, we can proceed by finding the general solution of the differential equation y" + 400π²y = 0. This is a second-order linear homogeneous differential equation, and its general solution can be obtained by assuming a solution of the form y = e^(rt), where r is a constant.

Substituting this assumed solution into the differential equation, we obtain the characteristic equation r² + 400π² = 0. Solving this quadratic equation yields two complex conjugate roots: r = ±20πi.

The general solution of the differential equation is then given by y(t) = C₁cos(20πt) + C₂sin(20πt), where C₁ and C₂ are constants.

Next, we apply the boundary conditions y(0) = 0 and y'(1) = 1 to determine the specific values of the constants C₁ and C₂. However, when we substitute y(0) = 0, we find that C₁ = 0. Substituting y'(1) = 1 leads to an inconsistent equation.

Since we cannot find specific values for the constants C₁ and C₂ that satisfy the given boundary conditions, we conclude that the boundary value problem has no solution.

In summary, the given boundary value problem y" + 400π²y = 0, y(0) = 0, y'(1) = 1 is a homogeneous problem. However, after solving the differential equation and applying the boundary conditions, we find that there is no solution that satisfies both conditions.

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Answer:

the probability of picking two white socks is 1/3, or approximately 0.333.

Step-by-step explanation:

When choosing the first sock, there are 10 socks in total, and 6 of them are white. Therefore, the chance of picking a white sock on the first try is 6/10 or 3/5.

When picking the second sock, there are only 9 socks left in the drawer, since we did not replace the first sock. Of the remaining socks, 5 are white (since we did not replace the first white sock) and 4 are black. Therefore, the probability of picking a white sock on the second try, given that we picked a white sock on the first try, is 5/9.

Answer:  1/3

Step-by-step explanation:6*5/2 is number of ways that work. This is 15. There are 10*8/2=45 total ways. 15/45=1/3.

The required proportional ratio is y = 0.08 x. gives Halona 23 minutes to move her 1.93 kilometers to her neighbor's house. As long as you move at a steady pace.

How many kilometers Halona can run in x minutes y expressed as a ratio. Then find y in percentage. The relationship between two or more proportional or inversely proportional sets of values, whether they are directly related or not, is called proportionality.

Here we have

Substitute k into the proportional equation.

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To develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals, you can follow these steps:

1. Create a spreadsheet with columns for the team names, points scored by each team, and the difference in their point totals.
2. Assign a cell to represent the average points scored by the Iowa Wolves. Let's say it's cell A1.
3. Assign a cell to represent the standard deviation of points scored by the Iowa Wolves. Let's say it's cell A2.
4. Use the "=NORM.INV(RAND(), A1, A2)" formula in a cell to generate a random value representing the points scored by the Iowa Wolves in a particular game.
5. Repeat step 4 for each game or simulation you want to run, populating the points scored by the Iowa Wolves in the respective cells.
6. Calculate the average of the generated points scored by the Iowa Wolves by using the "=AVERAGE()" formula on the range of cells containing the simulated points.
7. Calculate the standard deviation of the generated points scored by the Iowa Wolves by using the "=STDEV()" formula on the same range of cells.

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Answer:

3x-$150

Step-by-step explanation: