A probability density function of a random variable is given by f(x)=6x7 on the interval [1, co). Find the median of the random variable, and find the probability that the random variable is between t

Answer:

2.8888888888889

Step-by-step explanation:

I hope this helps

Answer:

2.8889 I searched it and I found this I hope this is what you're looking for

Working together, they can complete the task in 4 hours and 48 minutes.

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

Tracy needs 8 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/8 hours = 1/8 task per hour.

This means that she can complete 1/8 of the task per hour.

Dave needs 12 hours to complete the task, then his ratio is:

1 task/12 hours = 1/12 task per hour.

This means that he can complete 1/12 of the task in one hour.

If they work together, then the ratios can be added:

R = \(\frac{1}{8}\) +  \(\frac{1}{12}\)

  = \(\frac{3+2}{24}\)

  = \(\frac{5}{24}\)

So, working together, in one hour they can complete  \(\frac{5}{24}\) of the task, now we can find the number of hours needed to complete the task as:

\(\frac{5}{24}\)×\(x\)= 1 task

x = \(\frac{24}{5}\) hours = 4.8 hours

knowing that an hour is 60 minutes, then 0.8 of an hour is 60*0.8 = 48 minutes.

Then x = 4 hours and 48 minutes.

To learn more about Time and work from the given link:

https://brainly.com/question/16900783

#SPJ4

Answer:

The speed of Sara is 78.4 km/h.

Step- by-step explanation:

Manuel and Sara travel a certain distance, and the times they use are in the ratio 21/15. Manuel's speed is 56km / h. What is Sara's speed?

Let the distance is d.

speed of Manuel = 56 km/h

time taken by Manuel = 21 t

time taken by Sara =  15 t

Let the speed of Sara is v.

Distance = speed x time

For Manuel:

d = 56 x 21 t ..... (1)

For Sara:

d = v x 15 t ..... (2)

From (1) and (2)

56 x 21 t = v x 15 t

v = 78.4 km/h

Answer: The snake needs to find a heat source to regulate its body temperature

Step-by-step explanation:

Answer:

Snakes maintain homeostasis through their body structures and reptile behavior. They regulate their balance by basking in the sun.

Step-by-step explanation:

the probability that exactly 2 seeds don't grow out of 8 seeds planted is approximately 0.1907 or 19.07%.

To calculate the probability that exactly 2 seeds don't grow out of 8 seeds planted, we can use the binomial probability formula. The formula for the binomial probability is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of exactly k successes (in this case, seeds not growing),

n is the total number of trials (seeds planted),

k is the number of successes (seeds not growing),

p is the probability of success (seeds not growing), and

C(n, k) is the number of combinations of n items taken k at a time.

In this scenario:

n = 8 (seeds planted)

k = 2 (exactly 2 seeds don't grow)

p = 0.15 (probability of a seed not growing, which is 1 - 0.85)

Let's calculate the probability:

P(X = 2) = C(8, 2) * 0.15^2 * 0.85^(8-2)

Using the combination formula C(n, k) = n! / (k! * (n-k)!) to calculate the number of combinations:

C(8, 2) = 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28

Now, let's substitute the values into the formula:

P(X = 2) = 28 * 0.15^2 * 0.85^6

Calculating the result:

P(X = 2) = 28 * 0.0225 * 0.3012 ≈ 0.1907

To know more about probability visit;

brainly.com/question/31828911

#SPJ11

The range of the function g(x) is [300, ∞)

In this question, we have been given that we have deposited $300 into a savings account that earns interest annually.

The function g(x) = 300(1.04)^x used to find the amount of money in the savings account, g(x), after x years.

We need to find the range of the function.

Since a savings account earns interest annually, x can have take values from 0 to infinity.

For x = 0 year,

g(0) = 300(1.04)^0

g = 300 * 1

g = 300

For x tends to ∞, the value of function would be ∞

Therefore, the range of the function g(x) is [300, ∞)

Learn more about the range here:

https://brainly.com/question/27032480

#SPJ1

Answer:

0

Step-by-step explanation: because there’s no info

The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3

From the question, the expression is given as

k/3+16

Start by factoring 1/3 out of the first term

So, we have the following expression

1/3k + 16

The above is one of the ways of rewriting the expression

Another way is by taking the LCM

So,we have

k/3+16 = (k + 48)/3

Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3

Read more about equivalent expressions at

https://brainly.com/question/2972832

#SPJ1

The expression equivalent to x⁶ - 9 is : (x³)² - 3²

A statement is considered to be an expression if it contains at least two numbers or variables and one mathematical action.

Power is the factor that is multiplied by itself, and exponent is the number of times the same base number has been multiplied.

Calculation:

we have given ,

x⁶ - 9

now we know that,

(xᵃ)ᵇ - yᵇ

similarly,

(x³)² - 3² = x⁶- 9.

To know more about expression visit to :

https://brainly.com/question/1859113

#SPJ1

Rounding to three decimal places, the critical value is ±2.109.

The critical value for a 95% confidence interval, we need to look up the t-distribution with degrees of freedom given by:

df = [(s1²/n1 + s2²/n2)²] / [((s1²/n1)²/(n1-1)) + ((s2²/n2)²/(n2-1))]

s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.

Plugging in the values given in the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

Using a t-distribution table or a calculator, we can find the critical value for a 95% confidence interval with 17 degrees of freedom:

\(t_c\) = ±2.109We must get the crucial value for a 95% confidence interval using the degrees of freedom provided by the following t-distribution:

(S12/n1 + S22/n2)2 = df ((s22/n2)2/(n2-1)) + ((s12/n1)2/(n1-1))))

The sample standard deviations are s1 and s2, and the sample sizes are n1 and n2.

Inserting the values from the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

We may get the crucial value for a 95% confidence interval with 17 degrees of freedom using a t-distribution table or a calculator:

For similar questions on decimal places

https://brainly.com/question/28393353

#SPJ11

Answer:

1/3

Step-by-step explanation:

P(Sport utility vehicle) = 2/6 = 1/3

The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

Learn more about rectangle on

https://brainly.com/question/2607596

#SPJ1

Answer:

24

Step-by-step explanation:

x + 16

8 + 16

= 24

You just plug in 8 in the x place. Hope this helps, thank you !!

The solution to the equation 9 × (3 ÷ x) = 26 is x = 1.038.

To solve the equation 9 × (3 ÷ x) = 26 for x, we can follow these steps:

Simplify the expression on the left side of the equation:

9 × (3 ÷ x) = 26

27 ÷ x = 26

Multiply both sides of the equation by x to eliminate the division:

(27 ÷ x) × x = 26 × x

27 = 26x

Divide both sides of the equation by 26 to solve for x:

27 ÷ 26 = (26x) ÷ 26

1.038 = x

As a result, x = 1.038 is the answer to the equation 9 (3 x) = 26.

for such more question on equation

https://brainly.com/question/17482667

#SPJ8

Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

\(15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0\)

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

To learn more about motion visit:

https://brainly.com/question/27102563

#SPJ4

We have a function f(x) and we have to find its inverse.

f(x) is defined as:

Let define g(x) as the inverse of f(x), then we have that:

Answer:

0.038

Step-by-step explanation:

Answer:sThe correct answer is 11

Step-by-step explanation:

I just took the test just trust me

Emily's commute would be shorter than 21 minutes about 11 times per year.

Here,

we have to use the normal distribution formula,

⇒ Z = (X - μ) / σ

where,

Z = the z-score

X = the value we're interested in (in this case, 21 minutes)

μ = the mean (25 minutes)

σ = the standard deviation (2.5 minutes)

First, we need to find the z-score,

⇒ Z = (21 - 25) / 2.5 Z

       = -1.6

Now, we need to find the area under the normal curve to the left of the z-score.

Use a z-score table to do this calculation.

⇒ P(Z < -1.6) = 0.0548

This means that the probability of Emily's commute being shorter than 21 minutes is 0.0548, or 5.48%.

Finally, we need to find how many times out of 203 days this would happen.

Multiplying the probability by the number of days,

⇒ 0.0548 x 203 = 11.13

Hence, to the nearest whole number, Emily's commute would be shorter than 21 minutes about 11 times per year.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ2

Applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

A parallelogram is a quadrilateral that has two pairs of opposite sides that are congruent to each other.

Given the following:

Find x by creating an equation:

PQ = RS (congruent sides)

Substitute

9x + 1 = 13x - 11

Combine like terms

9x - 13x = -1 - 11

-4x = - 12

x = 3

Therefore, applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

Learn more about parallelogram on:

https://brainly.com/question/4314341

The quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line

Taylor polynomial function simply refers to an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

So therefore, the quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line

Learn more about Taylor polynomial function:

https://brainly.com/question/2533683

#SPJ4

Answer:

34/50 or 68% or 0.68

Step-by-step explanation:

S= {16, 12, 22}

16 + 12 + 22 = 50

50 - 16 = 34

34/50

or

68%

or

0.68

Answer:

135

Step-by-step explanation:

l x w x h

Answer:

B

Step-by-step explanation:

Draw a line from the top of the 3 m line to the 10 m line so that the new line meets the the 10 meter line at right angles. The part you are interested in should be 4 meters long.

Top rectangle.

Area = L * W

L = 7  (10 - 3 = 7)

W = 4

Area = 4* 7 =                                       28

Bottom rectangle

Area = L * W

L = 12

W = 3

Area = 12 * 3                                      36

Total Area                                          64

w = 28

solving stepwise:

\(\dashrightarrow \sf \ \ 34-w=6\)

\(\dashrightarrow \sf \ \ -w=6-34\)

\(\dashrightarrow \sf \ \ -w=-28\)

\(\dashrightarrow \sf \ \ w=28\)

Answer:

Step-by-step explanation:

Given equation:

Substact 6 both sides:

Subtract 28 both sides:

Multiply -1 both sides:

Answer:

4.51352cm

Step-by-step explanation:

Hope you could understand.

If you have any query, feel free to ask.

Answer: 63.28 percent of the SAT verbal scores are less than 550.

To find the percent of SAT verbal scores that are less than 550, we need to find the z-score and use the standard normal table to find the corresponding percentile.

First, let's find the z-score:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.

For this problem, x = 550, μ = 513, and σ = 109. Plugging in these values, we get:
z = (550 - 513) / 109
z = 0.339

Next, we can use the standard normal table to find the percentile corresponding to this z-score. The table gives us the area to the left of the z-score, which is the same as the percent of scores that are less than 550.

Looking up 0.339 on the standard normal table, we find that the corresponding percentile is 0.6328, or 63.28%.

Therefore, 63.28% of the SAT verbal scores are less than 550.

To know more about percent click here:

https://brainly.com/question/19034579

#SPJ11