Provide the missing reasons for the proof.

Given: AB || RS

Prove: QA/QR = QB/QS

a) the probability that exactly one of the people becomes ill = \(\frac{3}{8}\)

b) the probability that at least two of the people become ill = \(\frac{1}{2}\)

c) The probability that none of the three people becomes ill = \(\frac{1}{8}\)

Given that

three people have been exposed to a certain illness. once exposed, a person has a 50-50 chance of actually becoming ill.  

the outcome = \(2^{3}\) = 8

a) the probability that exactly one of the people becomes ill:

there are 3 persons to find probability exactly one need to be ill let's consider 1st person maybe ill and there is a chance that 2nd person is ill if not 2nd person 3rd person is ill

P(a) = \(\frac{1 + 1 + 1}{8}\)

      = \(\frac{3}{8}\)

b) the probability that at least two of the people become ill

  The probability that exactly two people become ill is P2 = \(\frac{3}{8}\)

   the probability that exactly three

   people become ill is P3 =   \(\frac{1}{8}\)

   Therefore, the probability that at least two people become ill is

   P2 + P3 = \(\frac{3}{8}\)+ \(\frac{1}{8}\)

  =\(\frac{1}{2}\)

c)  The probability that none of the three people becomes ill is  \(\frac{1}{8}\)

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The lamina is bounded by the graphs of the equations y = x3, y = 0, and x = 2. The density of the lamina is given by ρ = kx. The mass and center of mass of the lamina need to be determined.

To find the mass of the lamina, we need to calculate the double integral of the density function ρ = kx over the region bounded by the given equations. Since the density is given by ρ = kx, it means that the mass per unit area increases linearly with x. Therefore, the density is higher at points with larger x-values.

To find the center of mass (X, Y), we need to calculate the moments of the lamina. The moment about the y-axis (Mx) is given by the double integral of x times the density function ρ = kx over the region, and the moment about the x-axis (My) is given by the double integral of y times the density function ρ = kx over the region. The center of mass coordinates (X, Y) can then be calculated using the formulas X = Mx/m and Y = My/m, where m is the mass of the lamina.

To determine the exact values of the mass and center of mass, the specific value of the constant k needs to be provided. Without knowing the value of k, we cannot calculate the mass or the center of mass.

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(a) The probability that exactly two of the four components last longer than 1,000 hours is 0.3679

(b) The probability that the subsystem operates longer than 1,000 hours is 0.8130

(a) Let X be the number of components that last longer than 1,000 hours. Then X follows a binomial distribution with n = 4 and p = 0.55 (the probability that a component lasts longer than 1,000 hours is 1 - 0.45 = 0.55). The probability that exactly two of the four components last longer than 1,000 hours is

P(X = 2) = (4 choose 2) × 0.55^2 × 0.45^2 = 6 × 0.3025 × 0.2025 = 0.3679

So the probability that exactly two of the four components last longer than 1,000 hours is 0.3679 (rounded to four decimal places).

(b) The subsystem will operate if any two of the four components are operating. This means that the subsystem will fail if either none or only one component is operating. Let Y be the number of components that are operating. Then Y follows a binomial distribution with n = 4 and p = 0.45 (the probability that a component fails in less than 1,000 hours is 0.45). The probability that none of the four components are operating is

P(Y = 0) = 0.45^4 = 0.0081

The probability that exactly one of the four components is operating is

P(Y = 1) = (4 choose 1) × 0.55 × 0.45^3 = 0.1789

Therefore, the probability that the subsystem fails is

P(failure) = P(Y = 0) + P(Y = 1) = 0.0081 + 0.1789 = 0.1870

So the probability that the subsystem operates longer than 1,000 hours is

P(success) = 1 - P(failure) = 1 - 0.1870 = 0.8130 (rounded to four decimal places).

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There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

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Answer:

5 times x minus 8 minus 7

Step-by-step explanation:

whenever you see an x right next to a number, it means that it's being multiplied for that number. For example: 2x mean 2 times x

This symbol - is a minus symbol. So when it's in front of a number, you say "minus" and then the number. For example: 4 - 3 means, Four minus three.

Answer:

6.75L of fuel are needed

Step-by-step explanation:

To solve this question we need to convert the miles to km and the gallons to liters in order to find the km/L that the car is doing:

km -1km = 0.621371miles-

449.6miles * (1km / 0.621371 miles) = 723.56km

L -1L = 0.264172gal-

12.9gal * (1L / 0.264172gal) = 48.83L

km/L:

723.56km / 48.83L= 14.82km/L

The liters the car takes to go 100km are:

100km * (1L / 14.82km) = 6.75L of fuel are needed

Answer:

B) 1/2 barrel/hour

Step-by-step explanation:

1/3 divided by 2/3 = 1/3 * 3/2 = (1*3)/(3*2) = 3/6 = 1/2, therefore the correct unit rate is B) 1/2 barrel/hour

Answer:

1/2

Step-by-step explanation:

1/3 x 3/2 = 1/2

if the train line is 130 kilometers long, it took 0.9 hour  time  before the two trains meet

A freight train on the bluepoint-vindale line departs bluepoint, traveling at a speed of 42 kilometers per hour.

at the same time, a second train leaves vindale, bound for bluepoint, and is moving at speed of  97 kilometers per hour.

if the train line is 130 kilometers long, distance is 130km

how much time will pass before the two trains meet?

Time = Distance /speed

Let the encounter take time x

the sum of the distance between two trains when they meet is 130 km

42x +97 x=130

139x =130

  x= 0.9 hour

Hence it took 0.9 hour before the two trains meet.

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Answer: 4a

Step-by-step explanation:

Answer:

a = 2

Step-by-step explanation:

2a + 2 = 6

2a + 2 - 2 = 6 - 2

2a = 4

2a / 2 = 4 / 2

a = 2

Hope this helps and I would appreciate if you give me the brainlist or not, thank you :) !!

Answer:

B. 0

Step-by-step explanation:

Your welcome :)

Answer:

b.0

Step-by-step explanation:

i got it right

Answer:

x = 3

Step-by-step explanation:

If you move -2 to the right side of the equation, you get:

4x = 12

Divide both sides by 4, and you get:

x = 3.

Answer:

- x= 10-6y+y²

Step-by-step explanation:

|x-1|=3-y

(|x-1|)²=(3-y)²

x-2x+1=9-6y+y²

-x=9-6y+y²+1

Step-by-step explanation:

draw a straight line then put four points on the straight line

Descriptive statistics are used to summarize data in a useful and informative manner.

This type of statistics provides meaningful information about the data set by organizing and presenting it in an easily understandable format. Descriptive statistics can be used to summarize the data in the form of tables, graphs, and charts. It can also be used to provide detailed information about the data set, such as the mean, median, mode, standard deviation, and range.

Descriptive statistics can also be used to make inferences about a population. This is done by comparing the data collected from a sample to the characteristics of the population. By understanding the characteristics of the population, researchers can make accurate predictions about the behavior of the population.

Descriptive statistics can also be used to determine if the data adequately represent the population. This involves analyzing the sample size, data accuracy, and the assumptions made about the population. If the data does not accurately represent the population, then researchers have to make changes to their data collection process or revise their assumptions about the population.

Finally, descriptive statistics can be used to gather or collect data. This involves designing surveys, experiments, and other data collection methods. By using descriptive statistics to collect data, researchers can ensure that the data is valid and reliable.

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Answer:

i may need more info on the temperature or do you have to find out

Step-by-step explanation:

The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

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Answer:

4 foot

Step-by-step explanation:

divide by 12

The equations N1/dt = r1N1[(K1 - N1 - ON2)/K1] and ON2/dt = r2N2[(K2 - N2 - BN1)/K2] describe models for population dynamics. These models are used to understand how populations of organisms change over time, based on factors like birth rates, death rates, and available resources.

In these equations, N1 and N2 represent the population sizes of two interacting species. The variables r1 and r2 are the intrinsic growth rates of these species, or the rates at which they reproduce in the absence of limiting factors. K1 and K2 represent the carrying capacities of the environment for each species, or the maximum population sizes that can be sustained by available resources.
The terms ON2 and BN1 represent the effects of interspecific interactions on population growth. ON2 refers to the negative impact of species 2 on the growth rate of species 1, and BN1 refers to the negative impact of species 1 on the growth rate of species 2. These interactions can take many forms, such as competition for resources or predation.
By manipulating these equations, scientists can make predictions about how populations will change over time, and test these predictions against real-world data. These models are particularly useful for understanding how species interact in complex ecosystems, and how human activities like habitat destruction and climate change are affecting these ecosystems.

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Answer:

$238

Step-by-step explanation:

Find the unit rate

$85 / 5 tutoring sessions = $17 / tutoring session

Multiply unit rate by 14 sessions

$17 / tutoring session * 14 tutoring sessions = $238

Answer:

$238 for 14 sessions

Step-by-step explanation:

If you pay $85 for 5 sessions, you need to find the unit rate, which is how much money for 1 session.  You find this out by dividing 85 by 5

85 / 5 = 17

It costs $17 for 1 tutoring session.  

Pete wants to know how much he will have to pay for 14 sessions.  When the sessions are $17 each, you would multiply 17 and 14

17 x 14 = 238

Pete would have to pay $238 for 14 tutoring sessions.

Answer: 9,000

Step-by-step explanation:

The angles that are supplementary angles are: ∠SRT and ∠SRO

Angles that are supplementary will give us a sum of 180 degrees when we add the two angles together. One is the supplement of the other.

Some examples of angles that are supplementary angles that are formed when two parallel lines are intersected by a transversal include:

Angle SRT and angle SRO are angles that are adjacent to each other because they share a common side SR and a common vertex R. They line on the straight line OT.

Therefore, angle SRT and angle SRO are two angles that are supplementary angles as shown in the diagram attached below where lines NP and QS are parallel lines. The supplementary angles are therefore angle SRT and angle SRO.

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Answer:

the answr is b

Step-by-step explanation:

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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The density is constant, we can pull it out of the integral. So, we have: mass = density * integral of area. To find the mass of the plate, we can integrate the area times the density.

Since the curve \(y = x^2\) is a function of x, we can use the following formula to find the area between the curve and the x-axis:

area = integral from a to b of [f(x) - g(x)] dx where f(x) is the upper function (in this case, \(y = x^2\)),

g(x) is the lower function (the x-axis), and a and b are the limits of integration (0 and 2, in this case).

So, we have: area = integral from 0 to 2 of [\(x^2\) - 0] dx= integral from 0 to 2 of \(x^2 dx= [x^3/3]\)

from 0 to \(2= (2^3/3) - (0^3/3)\)

= 8/3 \(cm^3\)

Now we can find the mass:

mass = density * area= 3 g/\(cm^2\) * (8/3) \(cm^3\)= 8 g

So the total mass of the plate is 8 g.(b)

To sketch the plate, we need to plot the curve \(y = x^2\) and shade in the region bounded by the curve and the x-axis from x = 0 to x = 2.

This region is a parabolic shape with a base of 2 cm and a height of 4 cm (since \(y = x^2\) and y = 0 when x = 0 and x = 2).

So the area of the plate is a triangle with base 2 cm and height 4 cm, which has an area of (1/2)bh = (1/2)(2 cm)(4 cm) = \(4 cm^2\).

Since the density of the plate is 3 g/\(cm^2\), the mass is:

mass = density x volume= density x area x thickness.

Since the thickness is not given, we can't find the mass directly. However, we can say that the mass is proportional to the thickness, so if we double the thickness, the mass will double as well.

Therefore, we can't say whether a is greater than or less than 1.

(c) The moment of inertia of the plate about the x-axis is given by:

Ix = density * integral from a to b of y * (distance from y to x-axis)\(^2 dy\)

Since the plate has constant density,

we can factor it out of the integral:

Ix = density * integral from a to b of y * (distance from y to x-axis)^2 dy= density * integral from 0 to 2 of x^4 dx

= density * \([x^{5/5}]\) from 0 to 2

= density * \((2^{5/5})\)

= (3 g/\(cm^2\)) * \((32/5) cm^5\)

= 96/5 g \(cm^2\)

So

a = Ix/mass = (96/5) g \(cm^2\) / 8 g

= 12 \(cm^2\).

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The output obtained after executing the java code snippet,

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

will be 4.

As per the question statement, we are provided with a java code snippet, which goes as:

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We will obtain an output of 4, as "++" is the post increment function.

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Answer:

E=118

K=50

Step-by-step explanation:

I=E

E=118

K=360-118-118-74 (sum of angles in quad)

K=50

If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28

As per the question statement, a random variable "z" follows a standard normal distribution.

We are required to determine the value of "k" such that the equation   [p(z > k) = 0.39] is satisfied.

To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,

Given, P(Z > k)  = 0.39

Or, P(Z < k) = (1 - 0.39)

Or, P(Z < k) = 0.61

Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28

Hence, (k = 0.28)

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Answer is 4th statement "Yes, the volume of the trophy is 433. 333 cm³".

To find the volume of the trophy,

Use the formula V = (1/3)xBxh,

Where B is the area of the base and h is the height.

Since the base of the trophy is a square with an edge of 10 cm,

its area is 10x10 = 100 cm².

The height of the trophy is the slant height of the pyramid, which is given as 13 cm.

Using the formula, we can calculate the volume of the trophy as,

V = (1/3)x100x13

   = 433.33 cm³.

Therefore, the answer is: Yes, the volume of the trophy is 433.33 cm², which is less than the 1,000 cm³ of aluminum available, so there is enough aluminum to cast the trophy.

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Answer:

it is option C

Step-by-step explanation:

Answer:

(2x+3)square+2

Step-by-step explanation:

(2x) square +2 (2x)(3)+(3)square

2x square +12x+9

I think so.

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