PLEASE HELP! THIS IS DUE!!!!

a) We would expect approximately 0.2325 × 200 = 46.5 vehicles

to fail in their first 2 years. Since we cannot have a fraction of a vehicle

failing, we would expect around 46 or 47 vehicles to fail in their first 2

years.

b) The approximate probability that 50 or more vehicles fail in

the first 2 years is 0.0004.

c) The approximate probability that no more than 10 of the remaining

vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.

a) The average lifespan of the vehicle is 8 years, and it follows an

exponential distribution, which has a probability density function of

\(f(x) = (1/θ) \times e^(-x/θ)\),

where θ is the mean of the distribution. Thus, θ = 8.

The probability that a vehicle fails in the first 2 years can be found by

integrating the exponential probability density function from 0 to 2:

P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx

Using a calculator or a table of integrals, we can find this probability to

be approximately 0.2325.

b) The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.

The probability that 50 or more vehicles fail in the first 2 years can be

found using the Poisson distribution with parameter λ = 46.5:

P(X ≥ 50) = 1 - P(X < 50)

Using a Poisson distribution table or a calculator, we can find that P(X <

50) is approximately 0.9996.

Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).

c) Given that 30 vehicles have already failed in under 2 years, we need

to find the probability that no more than 10 of the remaining 170 vehicles

fail in their first 2 years.

The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525

(rounded to 40).

Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable

with parameter λ = 40.

Using a Poisson distribution table or a calculator, we can find that P(Y ≤

10) is approximately 0.0002.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference of other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

To learn more about Triangle visit:

brainly.com/question/2773823

#SPJ4

The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference between the other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

To learn more about Triangle visit:

brainly.com/question/2773823

#SPJ4

9514 1404 393

Answer:

  a) y +2 = (4/3)(x -3)

  b) 4x -3y = 18

Step-by-step explanation:

a) The slope formula gives part of what is needed for point-slope form:

  m = (y2 -y1)/(x2 -x1)

  m = (2 -(-2))/(6 -3) = 4/3

Point-slope form is ...

  y -k = m(x -h) . . . . . . for slope m and point (h, k)

Using the first point, we get ...

  y +2 = 4/3(x -3)

__

b) Multiplying by 3 and eliminating parentheses, we get ...

  3(y +2) = 4(x -3)

  3y +6 = 4x -12

Adding 12 -3y to both sides gives ...

  18 = 4x -3y

Putting this in the usual form, we have ...

  4x -3y = 18

To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

Learn more about Cubic Formula here :

https://brainly.com/question/27377982

#SPJ11

The percent decrease is 10.16%

Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100

The first step is to calculate the decrease

= 4.33 - 3.89

= 0.44

The percent decrease can be calculated as follows

= 0.44/4.33 × 100

= 0.1016 × 100

= 10.16

Hence the percent decrease is 10.16 %

Read more on percent decrease here

https://brainly.com/question/28322662?referrer=searchResults

#SPJ1

Answer:

(B)  10.16%

Step-by-step explanation:

Correct on my quiz.

Answer:

7. Each sweatshirt is $60

8. Table is    3,60 and   5, 100  and   8,160  and   9,180  and     12,240

9. You would graph table by plotting the x,y coordinates of each point on a graph and connecting the dots to show linear relationship

Step-by-step explanation:

The values of the six trigonometric functions of θ are:

Sin θ = 4/√17Cos θ = √5Cot θ = 1/4Tan θ = 1/5Cosec θ = √17/4Sec θ = √(17/5)

Therefore, the correct answer is option A.

Given, the equation with a restriction on x is the terminal side of an angle 8 in standard position.

The equation is -4x+y=0 and x≥20.

The given equation is -4x+y=0 and x≥20

We need to find the trigonometric ratios of θ.

So, Let's first find the coordinates of the point which is on the terminal side of angle θ. For this, let's solve the given equation for y.

-4x+y=0y= 4x

We know that the equation x=20 is a vertical line at 20 on x-axis.

Therefore, we can say that the coordinates of point P on terminal side of angle θ will be (20,80)

Substituting these values into trigonometric functions we get the following:

Sin θ = y/r

= 4x/√(x²+y²)= 4x/√(x²+(4x)²)

= 4x/√(17x²) = 4/√17Cos θ

= x/r = x/√(x²+y²)= 20/√(20²+(4·20)²)

= 20/√(400+1600)

= 20/√2000 = √5Cot θ

= x/y = x/4x

= 1/4Tan θ = y/x

= 4x/20

= 1/5Cosec θ

= r/y = √(x²+y²)/4x

= √(17x²)/4x = √17/4Sec θ

= r/x

= √(x²+y²)/x= √(17x²)/x

= √17/√5 = √(17/5)

The values of the six trigonometric functions of θ are:

Sin θ = 4/√17

Cos θ = √5

Cot θ = 1/4

Tan θ = 1/5

Cosec θ = √17/4

Sec θ = √(17/5)

Therefore, the correct answer is option A.

To know more about trigonometric visit:

https://brainly.com/question/29156330

#SPJ11

Answer:

-2x+3 is the answer of this

Answer:

-2x+3  is the answer

Step-by-step explanation:

Answer:

axis of symm:  x = -1

vertex:  (-1, -4)

domain:  all real numbers

range:  y ≥ -4

x-intercepts:  1, 3

y-intercept:  -3

minimum at (-1, -4)

Step-by-step explanation:

the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

The coordinates of the vertices after a dilation with a scale factor of 1/3 centered at the origin is E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

Dilation is  a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that center of the dilation is origin.

Any coordinate (x, y) when dilated to a scale factor k is (kx, ky).

The coordinates of the quadrilateral are E(0, -6), F(9, -6), G(9, 3) and H(0, 3).

Dilation is with a scale factor of 1/3.

So all the coordinates become (1/3x, 1/3y).

E(0, -6) becomes E'(0, -2)

F(9, -6) becomes F'(3, -2)

G(9, 3) becomes G'(3, 1)

H(0, 3) becomes H'(0, 1)

Hence the coordinates are E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

Learn more about Dilation here :

https://brainly.com/question/13176891

#SPJ1

We have proven that p(x) is a valid pmf by demonstrating its non-negativity and the criterion for the sum of probabilities equaling 1.

To show that p(x) is a valid probability mass function (pmf), we need to demonstrate that it satisfies two properties: non-negativity and the sum of probabilities equaling 1.

1. Non-negativity: We need to show that p(x) is non-negative for all x.

Given p(x) = (m(m + 1))/(2^x), where x = 1, 2, 3, ..., m, we can observe that m and (m + 1) are positive since m is a fixed positive integer. Additionally, 2^x is positive for all positive integers x.

Therefore, p(x) = (m(m + 1))/(2^x) is a fraction with positive numerator and denominator, which implies p(x) is non-negative for all x.

2. Sum of probabilities equaling 1: We need to show that the sum of p(x) for all possible values of x is equal to 1.

We have p(x) = (m(m + 1))/(2^x), where x = 1, 2, 3, ..., m.

To find the sum of p(x) for x = 1 to m, we can evaluate the summation:

p(1) + p(2) + p(3) + ... + p(m) = (m(m + 1))/(2^1) + (m(m + 1))/(2^2) + (m(m + 1))/(2^3) + ... + (m(m + 1))/(2^m)

Factoring out (m(m + 1)) as a common factor, we get:

(m(m + 1))(1/2^1 + 1/2^2 + 1/2^3 + ... + 1/2^m)

Using the formula for the sum of a geometric series, we have:

(m(m + 1))(1 - (1/2^m))/(1 - 1/2)

Simplifying further

(m(m + 1))(2 - 1/2^m)

= m(m + 1)(2 - 1/2^m)

To complete the proof, we need to show that the above expression equals 1.

Since m is a fixed positive integer, the expression m(m + 1)(2 - 1/2^m) is also a positive number

Therefore, to satisfy the requirement of the sum of probabilities equaling 1, we need:

m(m + 1)(2 - 1/2^m) = 1

The above equation may not hold for all values of m. However, if we select a specific value of m that satisfies this equation, then p(x) = (m(m + 1))/(2^x) will be a valid pmf.

In summary, to show that p(x) is a valid pmf, we have demonstrated its non-negativity and the condition for the sum of probabilities equaling 1. The validity of p(x) as a pmf depends on choosing an appropriate value of m that satisfies the equation m(m + 1)(2 - 1/2^m) = 1.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

Answer: Type I error and Type II error are associated with hypothesis testing, where we test a hypothesis by collecting data and analyzing it.

For the given hypothesis, we can set up the null hypothesis as follows:

H0: The percentage of households with Internet access is less than or equal to 60%.

And the alternative hypothesis as:

Ha: The percentage of households with Internet access is greater than 60%.

Now, a Type I error occurs when we reject the null hypothesis (i.e., conclude that the percentage of households with Internet access is greater than 60%) when it is actually true. This means that we would be making a false claim that the percentage of households with Internet access is greater than 60%, when it is not.

On the other hand, a Type II error occurs when we fail to reject the null hypothesis (i.e., conclude that the percentage of households with Internet access is less than or equal to 60%) when it is actually false. This means that we would be missing the truth that the percentage of households with Internet access is greater than 60%.

So, in the context of the given hypothesis, a Type I error would be to conclude that the percentage of households with Internet access is greater than 60% when it is actually less than or equal to 60%, and a Type II error would be to fail to conclude that the percentage of households with Internet access is greater than 60% when it is actually greater than 60%.

Let x = the number of games. The problem can be rewritten as a system of equations:

Person 1 = 72.48 + 6x

Person 2 = 18.08x

We are looking for when the number of games for both are the same; so:

72.48 + 6x = 18.08x

Then:

72.48 = 18.08x - 6x

72.48 = 12.08x

x = 72.48/12.08

x = 6

Answer:

three point eighty two

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

To know more about marginal utility related question visit:

https://brainly.com/question/30841513

#SPJ11

Answer in standard form:  2x+y = 3

Answer in slope intercept form:   y = -2x+3

Both equations describe the same line. Select one of those formats to write to your teacher.

=======================================================

Reason:

The equation 2x+y = 9 solves to y = -2x+9; it is of the form y = mx+b

The parallel line will also have a slope of -2. Parallel lines have equal slopes, but different y intercepts.

The slope-intercept answer is of the form y = -2x+b

Plug in (x,y) = (-1,5) and solve for b.

y = -2x+b

5 = -2*(-1)+b

5 = 2+b

3 = b

b = 3

We go from y = -2x+b to y = -2x+3 which is in slope intercept form.

Adding 2x to both sides gets us 2x+y = 3 which is in standard form.

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

To know more about probability  click on below link :

https://brainly.com/question/14210034#

#SPJ11

Butt Koko, this is the solution:

Original price = 19.99

Sale price = 15.99

Discount = 19.99 - 15.99 = 4.00

We can use Direct Rule of Three to calculate the percent of discount, this way:

Price Percent

19.99 100

4.00 x

___________________

4 * 100 = 19.99 * x

400 = 19.99x

x = 400/19.99

x = 20.01

The approximate percent discount on the frisbee is 20%

Answer:

So the sequence of the five numbers are;

10,26,74,218,650

Step-by-step explanation:

In this question, we are interested in building a sequence of 5 numbers given the initial term.

Okay, to build this sequence, we will need to look at the rule that guides the building of the new sequence:

The rule is that the next term is 4 less than 3 times the previous term.

Okay, let’s call the next term y, while the previous term is x.

Following what was specified in the question;

y = 3x -4

Recall; the next term(y) is 4 less (-4) than 3 times (3 multiplied by) the previous term (x)

So let’s start with the initial term of 10.

The next term will be;

y = 3(10) -4 = 30-4 = 26

The next term after 26 will be ;

y = 3(26) -4 = 78-4 = 74

The next term after 74 will be;

y = 3(74) -4 = 222-4 = 218

The next term after 218 will be;

y = 3(218) -4 = 650

Answer:

never similar please mark me

\(16.929 \: inches\)

Answer:

Yes, his collection will be complete by the time his grandfather visits

Step-by-step explanation:

Here, we want to know if his collection would be complete by the time his grandfather visits.

From the question;

he has collected 13 different quarters in 2.25 months

At the same rate, x different quarters will be collected in 9 months

Thus, mathematically;

x * 2.25 = 13 * 9

x = (13 * 9)/2.25 = 52

Thus, at this rate he would have collected 52 quarters in 9 months.

Since he has only 50 to collect, it means his collection would be complete by the time his grandfather visits

Answer:

x = 53 degree

Step-by-step explanation:

53 degree angle = x angle( alternate exterior angle)

Therfore, x = 53 degree

Mark as brainliest

The equation of the nth term is 4 + n.

The 75th term is 79.

It is a sequence where the difference between each consecutive term is the same.

Example:

5, 7, 9, 11, 13 is an arithmetic sequence.

We have,

5, 6, 7, 8, ,,,,,a(75),,,,,,,,

This is an arithmetic sequence.

a = 5

d = 1

Now,

The nth term of arithmetic is a + (n - 1)d.

So,

= 5 + (n - 1)1

= 5 + n - 1

= 4 + n

The nth term is 4 + n.

The 75th term.

i,e

For n = 75,

= 4 + n

= 4 + 75

= 79

Thus,

The equation of the nth term is 4 + n.

The 75th term is 79.

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ1

Answer:

7500

Step-by-step explanation:

force = Acceleration × Mass

1500×5=7500

Answer:

s=ut +atsq/2

120=4u+4sq

4u=104

u=26m/sec

Answer:

26 m/s

Step-by-step explanation:

Given

\(s = ut + \frac{1}{2} {at}^{2} \)

When a = 2 , s = 120 and t = 4

Then

\(120 = u \times 4 + \frac{1}{2} \times 2 \times {4}^{2} \\ 120 = 4u + 16 \\ 120 - 16 = 4u \\ 104 = 4u \\ u = \frac{104}{4} \\ u \: = 26

Hope it will help :)❤