There are 10 people taking part in a raffle.

Ann, Bob, Elsa, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.

Suppose that prize winners are randomly selected from the 10 people.

Compute the probability of each of the following events.

Event A: The first three prize winners are Soo, Ann, and Jim, regardless of order.

Event B: Ann is the first prize winner, Lena is second, and Bob is third.

Write your answers as fractions in simplest form.

P(A) =

?

P (B) =

Answer:

Step-by-step explanation:

(Sin27) / 11 = (sin x) / 15

cross multiply

15 sin27 = 11 sin x

keep in calculator as you divide 15sin27 by 11.

sin x = .6190779542

do sin ^ -1 (.6190779542) (It’s a key on the calculator.)

x = 38.25*

9514 1404 393

Answer:

  38.2°

Step-by-step explanation:

According to the equation you are give, ...

  sin(x)/15 = sin(27°)/11

Multiplying by 15 gives you ...

  sin(x) = 15·sin(27°)/11 ≈ 0.619078

The inverse sine function is used to find the angle x. It may show as sin⁻¹ on your calculator.

  x = arcsin(0.619078)

  x ≈ 38.2°

_____

Additional comment

x is shown in the figure as an acute angle, so that is the value we have chosen. The other angle that has sin(x) = 0.619078 is the supplement of this, or 141.8°. The two solutions are shown in the 2nd and 3rd attachments.

The area being measured will not match the Riemann sum. By employing ever smaller forms to divide the area more precisely, this mistake can be minimized. The sum approaches the area as the shapes become ever-smaller.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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Given a rectangle with the length of x+2 and width of 3x - 1. The area of a rectangle is given by the product of the length and width.

Thus, the area of this rectangle can be found as follows:Area = (x+2)(3x-1

Area = 3x^2 - x + 6x - 2

Area = 3x^2 + 5x - 2

Hence, we can express the area of the given rectangle in terms of the variable x as 3x^2 + 5x - 2. Therefore, the correct option is none of the provided options.

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Answer:

the area is 32 square inches

Step-by-step explanation:

you multiply both sides that have 9 because they are equal and then you add the 14 on

Answer:

63 Inches

Step-by-step explanation:

The formula for finding the area of a triangle is:

(b*h)/2

First, let's plug in the values.

(14*9)/2

Simplify...

126/2

Divide the two which gives us:

63

Therefore, the answer is:

63 Inches.

Hope this helps!

Answer:

im failing this too!

Step-by-step explanation:

guys pleadse we need gekp

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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The coordinates of K so that the ratio of JK to KL is of 2/7 are given as follows:

K(3,-4).

The coordinates of K are obtained applying the proportions in the context of the problem.

The ratio of JK to KL is of 2/7, hence the equation is given as follows:

K - J = 2/9(L - J).

Then the x-coordinate of K is obtained as follows:

x + 3 = 2/9(24 + 3)

x + 3 = 6

x = 3.

The y-coordinate of K is obtained as follows:

y - 4 = 2/9(-32 - 4)

y - 4 = -8

y = -4.

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Answer:

(-6, -7)

explanation:

The value of y will be negative and x value shall be same.

Here the original coordinates of A: (-6, 7)

so when reflected: (-6, (-)7) = (-6, -7)

Answer:

cos S=

√74/11..................

Using the test statistic, at the 0.05 level of significance, we do not find sufficient evidence to support the political scientist's claim and hence reject the null hypothesis.

To determine whether there is enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65%, we can perform a hypothesis test using the given data.

Let's set up the null and alternative hypotheses:

H₀: p ≤ 0.65 (Null hypothesis: The proportion of college students interested in election results is 65% or less)

Ha: p > 0.65 (Alternative hypothesis: The proportion of college students interested in election results is more than 65%)

We are given that the sample size is 265 college students, and out of this sample, 180 students say they're interested in their district's election results.

To perform the hypothesis test, we'll calculate the test statistic, which is the z-statistic in this case, using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

Where p is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

Let's calculate the sample proportion:

p = 180 / 265 ≈ 0.679

Now, we can calculate the test statistic:

z = (0.679 - 0.65) / √(0.65(1-0.65)/265) ≈ 1.295

Next, we'll compare the test statistic with the critical z-value at a 0.05 level of significance (α = 0.05) for a one-tailed test.

Using a standard normal distribution table or a statistical calculator, the critical z-value at α = 0.05 is approximately 1.645.

Since the test statistic (1.295) does not exceed the critical z-value (1.645), we fail to reject the null hypothesis. In other words, we do not have enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65% based on this sample.

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The function to calculate the speed is S = 260.52/t.

From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:

= 78 × 3.34

= 260.52km

The function to calculate the speed will be:

Speed = Distance/Time

S = 260.52/t

Complete question:

The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.

a. What is the total length of the race?

b. Write a function that can be used to model the race where the independent variable represent the average speed.

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Answer:

600 + 70 + 4 + .900 + .010 + .009

Step-by-step explanation:

you just break up the number to write it in expanded form.

Answer:

if your trying to find the area of 10ft and 2 1/2 all you gotta do is turn the 2 1/2 in a decimal and multiply it by 10 which is 25

Step-by-step explanation:

The bank's real rate of return for that year is 2.0%.

To calculate the real rate of return, we subtract the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 7% and the inflation rate is 5%.

Real rate of return = Nominal interest rate - Inflation rate

Real rate of return = 7% - 5%

Real rate of return = 2.0%

Therefore, the bank's real rate of return for that year is 2.0%.

The real rate of return represents the actual increase in purchasing power or wealth after adjusting for inflation. It measures the return on an investment after accounting for the effects of inflation.

In this scenario, the bank lends money at an interest rate of 7%. However, the inflation rate for that year is 5%. The inflation rate erodes the purchasing power of money over time. Therefore, to determine the bank's real rate of return, we subtract the inflation rate from the nominal interest rate.

By subtracting 5% (inflation rate) from 7% (nominal interest rate), we get a real rate of return of 2.0%. This indicates that the investment made with the bank has a real return of 2.0% after accounting for the effects of inflation.

It's important to consider the real rate of return when evaluating the profitability or value of an investment. The real rate of return reflects the true growth or decline in purchasing power and provides a more accurate assessment of the investment's performance.

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A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?​

step 1

Find the probability that Jill draw an A

P=2/5

step 2

Find the probability that jill draw a C

P=1/4

therefore

the probability that Jill will draw an A and then a C is

P=(2/5)(1/4)

P=2/20

The position vector that represents the velocity of the plane relative to the ground is \begin{pmatrix}40\\40\\-20\end{pmatrix}.

The position vector of the velocity of the plane relative to the ground

We will resolve the velocity of the airplane into two vectors, one in the North direction and the other in the East direction.

Let's assume that the velocity of the airplane in the North direction is Vn and in the East direction is Ve.

Vn = 40 mphVe = 40 mphIn the vertical direction, the airplane is moving downward due to downdraft.

The velocity of the airplane in the vertical direction isVv = -20 mph (- sign because it is moving downward)

The velocity of the airplane with respect to the ground (v) is the resultant of these three vectors (Vn, Ve, and Vv)

According to the Pythagorean theorem;

v^2 = Vn^2 + Ve^2 + Vv^2v = sqrt(Vn^2 + Ve^2 + Vv^2)

Putting values, we get

v = sqrt(40^2 + 40^2 + (-20)^2)

= sqrt(3200) mph

v = 56.57 mph

Therefore, the position vector that represents the velocity of the plane relative to the ground is \begin{pmatrix}40\\40\\-20\end{pmatrix}.

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Answer:

Step-by-step explanation:

Plot the points x-intercept and intercept on the graph. Join the two points to get the straight line. This is the graph of the linear equation.

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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For the equation x^3 + 27y^4 = In  y' at (-3, 1) is -27/107 by using implicit differentiation y' = 3x^2 / (y - 108y^3).

To find y' using implicit differentiation and then evaluate y' at (-3,1) for the given equation x^3 + 27y^4 = ln(y), follow these steps:

1. Differentiate both sides of the equation with respect to x, remembering to apply the chain rule when differentiating with respect to y.

d/dx(x^3) + d/dx(27y^4) = d/dx(ln(y))

2. Apply the chain rule on the right-hand side:

3x^2 + 27(4y^3)(dy/dx) = (1/y)(dy/dx)

3. Solve for dy/dx (which is y'):

dy/dx(y - 108y^3) = 3x^2

y' = dy/dx = 3x^2 / (y - 108y^3)

4. Evaluate y' at (-3, 1):

y'(-3, 1) = 3(-3)^2 / (1 - 108(1)^3)

y'(-3, 1) = 27 / (-107)

So, y' = 3x^2 / (y - 108y^3), and y'(-3, 1) = -27/107.

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Answer:

Reflection across x = -5

Answer:

Hi, there your answer is\(y=\frac{1}{2} x-4\)

Step-by-step explanation:

Let's solve for y.

3x−6y=24

Step 1: Add -3x to both sides.

3x−6y+−3x=24+−3x

−6y=−3x+24

Step 2: Divide both sides by -6.

−6y /−6 = −3x+24 /−6

y=1/2x-4

Hope this helps :)

The answer of modelled graph representing heights of the steps are:

a. Period = 40 sec.

b. Equation of axis :

        H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Peak is highest point of step of escalator.

d. Range ( -1, 5)

e. Domain ( 0, 350 )

f. No.

From the attached graph which represents the height of steps in escalator gave answer of the following question :

a. Period of the function = 40 sec.

It represents the complete cycle.

b. Equation of the axis for periodic function is given by breaking the graph into points :

H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Peak of the periodic function is given highest point of the escalator.

d. Range of the function is -1 to 5.

e. Domain for 10 cycles is ( 0, 350 ).

f. No , Steven is not correct. At t= 350s stair will  be at ground level.

Therefore, the answer based on the height of escalator steps through graph are:

a. Period of the function = 40 sec

b. Equation of axis for periodic function:

         H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Highest point of steps represents peak.

d. range = -1 to 5

e. Domain of periodic function : ( 0,350)

f. No.

The above question is incomplete, the complete question is :

1. Steven is monitoring the height of one particular step on an escalator that takes passengers from the ground level to the second floor. The height of the Height of Step step in terms of time can be modelled by the graph shown. a) What is the period of the function, and what does it represent in this situation? b) Determine the equation of the axis for this periodic function. c) What do the peaks of the periodic function represent in this situation? Time (s) d) State the range of the function. e) If the escalator completes only 10 cycles before being shut down, what is the domain of the periodic function? f) Steven states that the stair will be at ground level at  t = 300s. Is he correct? Justify your answer.

Graph is attached.

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The probability that they were both there at exactly 6:00 PM, given that they were there at the same time at some point during the day, is 1/54 or approximately 0.0185.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Let's first consider the total time window during which Roger and Stacy could have visited the fair simultaneously.

Since Roger stayed for 2 hours and Stacy stayed for 3 hours, the maximum possible time they could have overlapped is 2 hours for Roger and 3 hours for Stacy, which gives a total of 5 hours.

We can visualize the possible overlap window as a rectangle with width 2 (for Roger) and height 3 (for Stacy), starting at some random time between 12:00 PM and 9:00 PM, and extending for 5 hours.

The probability of this happening is the ratio of the area of a 1-hour window (which is 1/9 of the total area of the time window) to the area of the overlap window (which is 2x3 = 6).

So the probability that they were both there at exactly 6:00 PM, given that they were there at the same time at some point during the day, is:

= (1/9) / 6

= 1/54

Therefore, The probability that they were both there at exactly 6.00 pm: 1/54

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The complete question:

Roger and Stacy each go to the county fair on the same day. They each separately show up at a random time between 12:00 PM and 9:00 PM. Roger stays for 2 hours and Stacy stays for 3 hours.

Given that, at some time, Roger and Stacy were at the fair simultaneously, what is the probability that they were both there at exactly 6:00 PM?

Whether the two ratios are 2: 3 and 2: 3 or a proportion

4: 6 and 12: 18

\($\frac{4}{6}$\)   and

\($\frac{12}{18}=\frac{2}{3}$\)   and

2/3

=2: 3 and 2: 3

Yes the given two ratios form a proportion.

The complete question is:

Check whether the given two ratios form a proportion or not: 4: 6  12: 18

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Answer:

3

Step-by-step explanation:

Answer:

-7x^2-3x

Step-by-step explanation:

-x * 7x + (-x) * 3

-7xx-3x

-7x^2-3x