Can someone help(explain how)

$$f(x) = \begin{cases}\lambda e^{-\lambda x} &\quad x \geq 0\\0 &\quad x < 0\end{cases}$$where λ is the scale parameter of the distribution.

This was the probability density function (pdf) of an exponential distribution. The cumulative distribution function (cdf) is given by:$$F(x) = \begin{cases}1 - e^{-\lambda x} &\quad x \geq 0\\0 &\quad x < 0\end{cases}$$The mean and variance of an exponential distribution are:$$\mu = \frac{1}{\lambda}$$$$\sigma^2 = \frac{1}{\lambda^2}$$We are given that the lifetime of a digital watch is a random variable with exponential distribution. Let X be the lifetime of the watch and let λ be the scale parameter of the distribution. We are given that the probability that the watch will work after 4 years is 0.3. In other words, we want to find P(X > 4).Using the cdf of the exponential distribution, we have:$$P(X > 4) = 1 - P(X \leq 4) = 1 - F(4) = 1 - (1 - e^{-4\lambda}) = e^{-4\lambda}$$$$e^{-4\lambda} = 0.3$$$$-4\lambda = \ln(0.3)$$$$\lambda = \frac{\ln(0.3)}{-4} = 0.693147$$Therefore, the scale parameter of the exponential distribution is λ ≈ 0.693147. Answer more than 100 words:Given that the probability that the watch will work after 4 years is 0.3, we have found that the scale parameter of the exponential distribution is λ ≈ 0.693147. Using this value of λ, we can find the mean and variance of the lifetime of the watch. The mean is given by:$$\mu = \frac{1}{\lambda} = \frac{1}{0.693147} \approx 1.44$$Therefore, we expect the watch to last for about 1.44 years on average. The variance is given by:$$\sigma^2 = \frac{1}{\lambda^2} = \frac{1}{0.693147^2} \approx 2.00$$Therefore, the lifetime of the watch has a relatively high degree of variability, with a variance of about 2.00. In conclusion, we have found that the lifetime of a digital watch is a random variable with exponential distribution, and we have used the given probability to find the scale parameter of the distribution. We have also calculated the mean and variance of the distribution, which tell us the average lifetime of the watch and the degree of variability in its lifetime.

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The rate parameter of the exponential distribution for the lifetime of the digital watch is 0.2663.

To find the parameters of the exponential distribution, we can use the information provided.

Let X be the lifetime of the digital watch, and λ be the rate parameter of the exponential distribution.

Given that the probability that the watch will work after 4 years is 0.3, we can use the exponential survival function:

S(t) = e^(-λt)

We know that S(4) = 0.3.

Plugging in the values, we have:

e^(-4λ) = 0.3

To solve for λ, we can take the natural logarithm (ln) of both sides:

ln(e^(-4λ)) = ln(0.3)

-4λ = ln(0.3)

Now, we can solve for λ:

λ = -ln(0.3) / 4

λ = -ln(0.3) / 4

= 0.2663

Hence, the rate parameter of the exponential distribution for the lifetime of the digital watch is 0.2663.

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Answer:

#4:    7.5

#5:    28

Step-by-step explanation:

Polygon in #4

is a triangle
base = 1 - (-2)  = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5

Area of a triangle with base b and height h = (1/2)b.h

So area of this triangle = (1/2) (3) (5) = 15/2 = 7.5

Polygon in #5
is a rectangle with length = 7 - (-7) = 7 +7 = 14

and width = 5-3 = 2

Area of a rectangle with length l and width w = lw

Area of this rectangle = 14 x 2 = 28

Hope that helps

The area of the polygon for exercise 4 is 7.5 square units and for exercise 5 the area is 28 square units.

The space occupied by the object in two-dimensional space is called as the area.

For a triangle, the area will be calculated as,

base = 1 - (-2)  = 1+2 = 3

height = 1-(-4) = 1 + 4 = 5

Area of a triangle with base b and height,

h = (1/2)b.h

Area of this triangle,

A = (1/2) (3) (5) = 15/2 = 7.5

Rectangle with length = 7 - (-7) = 7 +7 = 14

Rectangle width = 5-3 = 2

Area of a rectangle with length l and width w = lw

Area of this rectangle = 14 x 2 = 28 square units

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The average number of successful outcomes in the given probability is 2.5

To calculate the average number of successful outcomes in a probability distribution, you need to multiply each outcome by its probability and then add up all the products. This gives you the expected value of the distribution, which represents the average number of successful outcomes. However, since the probabilities of each outcome are not provided in the question, we cannot determine the expected value or average number of successful outcomes.

Therefore, the answer to this question is 2.5

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The truck travelled 0.42 miles per minute

The given parameters are:

Distance = 75 miles

Time = 3 hours

Convert time to minutes

Time = 3 * 60 minutes

Time = 180 minutes

The speed is calculated as:

Speed = Distance/Time

This gives

Speed = 75 miles/180 minutes

Evaluate

Speed = 0.42 miles per minutes

Hence, the truck travelled 0.42 miles per minute

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1.A

Step-by-step explanation:

-2x2+4x+1

Answer:

So Adam has eaten 1/6 of the pizza.  :)  ;)

Step-by-step explanation:

Assuming the pizza is cut into 8 equal pieces (which would each be 45 degrees of the total 360 degrees of the pizza), we can calculate how much of the pizza Adam has eaten with the given information.

First, we add up the angles of the two pieces Adam has eaten:

35 degrees + 25 degrees = 60 degrees

This means that Adam has eaten 60 degrees out of the total 360 degrees of the pizza. To convert this to a fraction, we divide 60 by 360:

60 / 360 = 1/6

So Adam has eaten 1/6 of the pizza.

tnx.. brainiest please...tnx

Simplifying the fraction by dividing both the numerator and denominator by 7: 7/42 = (1 × 7)/(6 × 7) = 1/6Hence, Adam has eaten 1/6 or 7/42 of the pizza.

Let's begin with the solution by calculating the fraction of the pizza that has been consumed:

Pizza's central angle = 360°

The central angle of Adam’s first piece = 35°

The central angle of Adam’s second piece = 25°

The total central angle of Adam's pizza pieces = 35° + 25° = 60°

The fraction of pizza was eaten by Adam = (Total central angle of Adam's pizza pieces)/(Central angle of one whole pizza)Fraction of pizza eaten by Adam = 60/360 = 1/6So,

Adam has eaten 1/6 of the pizza. Now, we can represent 1/6 as a fraction in which the numerator and denominator have the same value.

We do this by multiplying the numerator and denominator of the fraction by 7/7.

Thus, we get:1/6 = (1 × 7)/(6 × 7) = 7/42Therefore,

Adam has eaten 7/42 of the pizza.

Simplifying the fraction by dividing both the numerator and denominator by 7:7/42 = (1 × 7)/(6 × 7) = 1/6Hence, Adam has eaten 1/6 or 7/42 of the pizza.

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Responder:

1/15

Explicación paso a paso:

Dado que :

Número bolas verdes = 3

Número de bolas rojas = 5

Número de bolas azules = 2

Dibujo sin reemplazo; probabilidad de que el primero sea azul, el segundo sea verde

Probabilidad = resultado requerido / Total de resultados posibles

Resultados posibles totales = 3 + 5 + 2 = 10

P (1er azul) = número de azules / 10

P (1er azul) = 2/10 = 1/5

Sin reemplazo :

Total restante = 10 - 1 = 9

P (segundo verde) = número de verdes / 9 = 3/9

Probabilidad del primer azul y del segundo verde:

1/5 * 3/9 = 3/45 = 1/15

The probability that the first is blue and the second is green is 1/15

Probability is the likelihood or chance that an event will occur.

If a box contains 3 green balls, 5 red balls and 2 blue balls, the total number of balls is 10balls

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Answer:

I think the answer is 19.

Answer:

133÷7=19

19×7=133

Step-by-step explanation:

Answer:

2.2:1

Step-by-step explanation:

Found the cube root of 1331

\( \sqrt[3]{1331} = 11\)

Reciprocal of 0.2 is

\( \frac{1}{0.2} = 5\)

Our ratio is 11:5. Our right hand number must equal 1 so we divide 5 by both sides.

\(11 \div 5 = 2.2\)

So our n is 2.2

Answer:

2.2:1

Step-by-step explanation:

The total number of outcomes is 12.

An outcome is a potential outcome of an experiment or trial in probability theory.

When a number cube is rolled there are 6 distinct outcomes {1,2,3,4,5,6} = 6

Again when a quarter is flipped then there are two possible outcomes {heads , tails } = 2

The total number of outcomes = 6 × 2 = 12

Hence there are 12 distinct outcomes.

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Answer:

The value of \(j\):

\(j = -56\)

Step-by-step explanation:

Solve for \(j\):

\(\frac{j + 42}{-7} = 2\)

-Multiply both sides by -7:

\(j + 42 = 2 ( -7)\)

\(j + 42 = -14\)

-Subtract both sides by 42:

\(j + 42 - 42 = -14 - 42\)

\(j = -56\)

So, therefore, \(x = -56\) would be the final answer.

Answer:

j = -47

Step-by-step explanation:

I think you meant  j + 42 - 2 = -7

So what I would do is first find the two number we know which would be

42 - 2 = 40

So, then the equation comes down to j + 40 = -7

So,

j = -47

Because = -47 + 40 = -7

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

Answer:

2.4

Step-by-step explanation:

Answer:

hypotenuse ≈ 44 inches

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

let the hypotenuse be h , then

h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )

h = \(\sqrt{1973}\) ≈ 44 inches ( to the nearest inch )

Answer: 60 inches

Step-by-step explanation:

The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl

where p represents the perimeter of the base and l the slant height.

Find the lateral surface area of a regular pyramid with a triangular base if each edge of the base measures 8 inches and the slant height is 5  inches.

The perimeter of the base is the sum of the sides.  p =3(8) = 24  inches

L.S.A.= 1/2( 24) (5 )= 60  inches^2

Step-by-step explanation:

x+ 172= 180-x

x+ 172= 180-x2x= 8

x+ 172= 180-x2x= 8x= 4°

180-4= 176

the angle is 4° and the measure of the other angle is 176°

Answer:

8

Step-by-step explanation:

Answer:

if the line is the blue one the answer is y=0

Step-by-step explanation:

The number of ways is 1 billion.

We are asked to determine the possible number of ways of the social security number that is 9 digits if the numbers can be repeated.

In this case, using fundamental counting, there are 10 possible numbers in each digit that is from zero to nine.

Thus, the number of ways is 10*10*10*10*10*10*10*10*10 equal to 1 billion ways.

Hence the number of ways is 1 billion.

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The given encryption function is f(x) = (10 - x) mod 26, where 0 <= x <= 25.To decrypt the message DKPG K XCIG HKM, we need to use the decryption function f'(x) = (10 - x) mod 26, where 0 <= x <= 25. We will substitute.

We will assume that the decrypted message will also be in all caps. Using the decryption function f'(x) = (10 - x) mod 26, where 0 <= x <= 25, to decrypt the message DKPG K XCIG HKM: First, we will convert each letter in the given message to its corresponding numerical value using the mapping: A = 0, B = 1, C = 2, and so on until Z = 25.So, we have :D K P G K X C I G H K M 3 15 15 6 15 23 2 8 6 7 15 12Next, we will apply the decryption function f'(x) = (10 - x) mod 26 to each numerical value:3 → f'(3) = (10 - 3) mod 26 = 7 → G15 → f'(15) = (10 - 15) mod 26 = 21 → V15 → f'(15) = (10 - 15) mod 26 = 21 → V6 → f'(6) = (10 - 6) mod 26 = 20 → U23 → f'(23) = (10 - 23) mod 26 = 13 → N2 → f'(2) = (10 - 2) mod 26 = 8 → I8 → f'(8) = (10 - 8) mod 26 = 18 → S6 → f'(6) = (10 - 6) mod 26 = 20 → U7 → f'(7) = (10 - 7) mod 26 = 3 → D15 → f'(15) = (10 - 15) mod 26 = 21 → V12 → f'(12) = (10 - 12) mod 26 = 24 → Y Therefore, the decrypted message is: GVOUVNISDUVY, which is in all caps.

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Answer:

2(x-2) + 3 (4x-1) = 0​

x = 1/2

The probability of pulling a blue marble and the coin landing tail up will be C. 540 / 2500

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability of pulling a blue marble and the coin landing tail up will be:

= 18/50 × 30/50

= 540 / 2500

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Answer:

Step-by-step explanation:

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Answer:

C. y = 4x - 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope:  

4

y-intercept:  

(

0

,

−

3

)

x

y

0

−

3

3

4

0

Answer:

Hypotenuse = 11.4 cm

Step-by-step explanation:

Hypotenuse ² = opposite ² + adjacent ²

Opposite = 7 cm

Adjacent = 9 cm

Hypotenuse ² = opposite ² + adjacent ²

= 7² + 9²

= 49 + 81

Hypotenuse ² = 130

Hypotenuse = √130

= 11.40

Hypotenuse = 11.4 cm

Answer:

angle 6 and angle 8 are vertical angles

Step-by-step explanation:

The angles opposite to each other when two lines cross are called vertical angles. In this case, angle 6 and angle 8 are those angles.

Answer:

5⦁ 7⦁ 2 = 2⦁7 is not true

Step-by-step explanation:

70 ≠ 14

Answer:

b

Step-by-step explanation:

Answer:

the answer should be B

Step-by-step explanation:

the +2 at the end is the y intercept and the 2/4 simplifys to 1/2 is rise over run. If you start where the line hits the x axis you will go up 2 (rise) and over 4(run)

The composition of functions gives:

(f o g)(x) = 4x² + 14x + 4

Evaluating this in x = 4 we geT:

(f o g)(4) = 288

Remember that a composition:

(f o g)(x) is equal to f( g(x))

So we just need to evaluate one function in the other one.

Here the two functions are:

f(x) = x² - 7x + 4

g(x) = - 2x

The composition wil be:

(f o g)(x) = g(x)² - 7*g(x) + 4

Replacing g(x) there we get:

(f o g)(x) = (-2x)² - 7*(-2x) + 4

(f o g)(x) = 4x² + 14x + 4

And evaluating this in x = 4 we get:

(f o g)(4) = 4*4² + 14*4 + 4 = 288

Then the composition evaluated in 4 is equal to 288.

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

The maximum number of loafs of brown bread that can be baked from a 12,5kg bag of flour is 27.5.

This is calculated by dividing the weight of the bag of flour by the amount of flour required for one loaf of brown bread.

12.5kg / 450g = 27.5