What is the mean speed of 5 swimmers in a race if their times were, in seconds: 22,22,28,30,36
?

Step-by-step explanation:

.7071 is the value to convert peak to RMS

Step-by-step explanation:

F( 1 ) = 2 - 6( 1 ) = - 4

F( 2 ) = 2 - 6( 2 ) = - 10

F ( 3 ) = 2 - 6( 3 ) = -16

There are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

To determine the number of ways the teams can finish first, second, third, and fourth in a league with 15 teams, we can use the concept of permutations.

For the first position, any of the 15 teams can finish first.

For the second position, there are 14 teams remaining that can finish second.

For the third position, there are 13 teams remaining that can finish third.

For the fourth position, there are 12 teams remaining that can finish fourth.

To calculate the total number of ways, we multiply the number of choices for each position:

Total number of ways = 15 * 14 * 13 * 12 = 32,760

Therefore, there are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

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The degree sequence of a graph is the list of degrees of its vertices arranged in non-increasing order.

For a bipartite graph $K_{m,n}$ with $m$ vertices in the first partite set and $n$ vertices in the second partite set, every vertex in the first partite set is connected to all vertices in the second partite set and vice versa. Therefore, the degree of each vertex in the first partite set is $n$ and the degree of each vertex in the second partite set is $m$.

So, the degree sequence of the bipartite graph $K_{m,n}$ is $n,n,\ldots,n$ (repeated $m$ times) followed by $m,m,\ldots,m$ (repeated $n$ times). In other words, the degree sequence consists of two blocks, each of length $m+n$, where the first block contains the degree $n$ repeated $m$ times and the second block contains the degree $m$ repeated $n$ times.

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Approximately 17 students who took the optional class passed their driver's test.

Let's solve this problem step by step.

We are given the following information:

28 out of 75 students who took the optional class passed their driver's test.

8 out of 15 students overall passed their driver's test.

3 out of 5 students took the optional class.

To find the number of students who took the optional class and passed, we need to calculate the intersection of these two groups.

First, let's calculate the total number of students who took the optional class:

Total students who took the optional class = (3/5) \(\times\) Total number of students

Total students who took the optional class = (3/5) \(\times\) 75 = 45

Now, let's calculate the total number of students who passed their driver's test:

Total students who passed their driver's test = (8/15) \(\times\) Total number of students

Total students who passed their driver's test = (8/15) \(\times\) 75 = 40

Next, let's find the number of students who both took the optional class and passed their driver's test.

This can be found by taking the intersection of the two groups:

Number of students who took the optional class and passed = (28/75) \(\times\)Total students who took the optional class

Number of students who took the optional class and passed = (28/75) \(\times\)45 = 16.8 (approximated to the nearest whole number).

Therefore, approximately 17 students who took the optional class passed their driver's test.

It's important to note that since we're dealing with whole numbers, the approximated answer is 17, as we cannot have a fraction of a student.

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Answer:

-12

Step-by-step explanation:

-1(-2)-14

2-14=-12

Answer:

-12

Step-by-step explanation:

you should give the other person brainliest

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

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Answer:

4−2x<−3

Step-by-step explanation:

check:

now --- 4°

after 1 hr --- 2°

after 2 hrs--- 0°

after 3 hrs--- -2°

after 4 hrs--- -4°

so between 3 and 4 hrs it will reach -3°

4-2x < -3

-2x < -7

x > 3 1/2

The player with a 39-inch vertical leap has a hang time of approximately 0.9014 seconds.

To determine the hang time of a player with a 39-inch vertical leap, we'll use the hang-time function, which relates vertical leap to hang time.

Step 1: Convert inches to feet by dividing the vertical leap by 12 (since there are 12 inches in a foot).
39 inches ÷ 12 = 3.25 feet

Step 2: Use the hang-time function formula, which is: Hang Time = √(8 × Vertical Leap ÷ Gravity), where gravity is approximately 32 feet per second².
Hang Time = √(8 × 3.25 ÷ 32)

Step 3: Calculate the hang time.
Hang Time = √(26 ÷ 32) ≈ √(0.8125) ≈ 0.9014 seconds

The player with a 39-inch vertical leap has a hang time of approximately 0.9014 seconds.

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The the equation K = C + 273.15 when solved for c is C = K - 273.15

K = C + 273.15

K - 273.15 = C

Therefore,

C = K - 273.15

Complete question:

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.

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Answer:

When solved for C, the equation is

C = K – 273.15

Step-by-step explanation:

The lower sum for f(x)=sin(x) over the interval [0,π/2] with n=6 is 0.4361. This method of dividing the interval into subintervals and using the left endpoint as the sample point is known as the left Riemann sum.

To find the lower sum for f(x)=sin(x) over the interval [0,π/2] with n=6, we need to divide the interval into six equal subintervals of length Δx=π/12. Then, we choose the left endpoint of each subinterval as our sample point and calculate the sum of the areas of the six rectangles formed. Thus, the lower sum is given by:

L = Δx [f(0) + f(π/12) + f(π/6) + f(π/4) + f(5π/12) + f(π/3)]

Substituting the values of the function, we get:

L = (π/12) [0 + 0.2588 + 0.5 + 0.7071 + 0.8660 + 0.9659]

L = 0.4361

Therefore, the lower sum for f(x)=sin(x) over the interval [0,π/2] with n=6 is 0.4361.

To find the lower sum for f(x)=sin(x) over the interval [0,π/2] with n=6, we divide the interval into six equal subintervals of length Δx=π/12. Then, we choose the left endpoint of each subinterval as our sample point and calculate the sum of the areas of the six rectangles formed. By substituting the values of the function, we get the lower sum as 0.4361.

The lower sum for f(x)=sin(x) over the interval [0,π/2] with n=6 is 0.4361. This method of dividing the interval into subintervals and using the left endpoint as the sample point is known as the left Riemann sum. This technique is useful for approximating the area under a curve and can be extended to find the upper sum and the definite integral.

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Answer:

2/9

Step-by-step explanation:

B

HOPE IT HELPS HAVE A GREAT DAY

Answer:

4/18 = 2/9 = 8/36

Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Assumed: expressions

Finding the expression with a value that is closest to e

Solution:

e is worth 2.718, which equals (1 + 1/19).

(1 + 1/19)^19

=> (20/19)^19 = 2.65

=> (1+ 1/22)^22

= >(23/22)^22 = 2.659

=> (1 + 1/20)^20

= >(21/20)^20 = 2.653

=>(1 + 1/21)^21

= > (22/21)^21 = 2.656

As a result, the value of e is closest to the value of 2.659.

Option B is hence the appropriate choice.

Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

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Answer: here is the answer I had to do file hosting

Step-by-step explanation: https://www.wattpad.com/story/34339632-5sos-boyxboy-smut

Answer:

y = -4x + (-3)      or       y = -4x - 3,

Step-by-step explanation:

So the symbol would be negative (-). The rest of the equation is constructed by adding the slope which is -4x to the y intercept which is -3

5.12% means

5.12/100 = 0.0512 (each year)

PreOwned Vehicle Cost = 31,100

For 5 years simple interest, the value would be:

31100 * 0.0512 * 5 = $7961.6

Total have to pay: 31,100 + 7961.6 = $39,061.6

The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

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Answer: 5(5w+6)

Step-by-step explanation:

Factor out a 5: 5(5w+6)

To check our work distribute: 25w+30

Answer: 5(5w+6)

Answer:

5 ( 5w + 5x )

Step-by-step explanation:

Just find a common factor in both terms: 5

5 ( 5w + 5x )

If you multiply again, you will see that the values of both expressions are the same.

7019 gallons of water will be in the pool.

Initial volume of water = 8000 gal

Daily reduction = 1.3%

Time = 10 days

Required equation:

=8000*(1- 0.013)^10

=8000*0.987^10

=7018.7781 ≈ 7019 rounded to the nearest gallon.

An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic. The definition of e necessitates an infinite number of algebraic operations, while the construction of is typically done as a geometric relationship.

Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

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According to a recent survey, nearly half of the respondents cited better pay as their primary reason for changing jobs.

The survey was conducted on a national level and the results indicate that a majority of people are looking to increase their earnings by switching jobs.

Other reasons are:

In conclusion, the survey clearly showed that the main reason for job changes among respondents was better pay. However, various other factors also play a role in an individual's decision to switch jobs, such as working conditions, career paths, and location.

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Answer:

1

Step-by-step explanation:

PEMDAS?  omg

Parenthesis, Exponents, Multiplication, Division ,Addition ,Subtraction

so we gon solve the parenthesis first. Basically, we will subtract 1 from 2.

(2-1)= 1

after dis we do dah exponents. we put 1 to the power of 6. 1*1*1*1*1*1= 1

1 to the 6th power is 1 :o

Answer:

your answer would be the second option.

Step-by-step explanation:

How this is is because it is in simple y=mx+b formation

the b is +1 and you go down one and over to the  three which is decreasing so it would be -1/3

1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

2. B. Type Ia supernovae

3. D. Downwards; towards the center of the Sun

The interpretation of the equations and the correct options for the given questions are as follows:

Question 1:

The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:

C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

Question 2:

To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:

B. Type Ia supernovae

Question 3:

Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:

D. Downwards; towards the center of the Sun

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The time taken for the T-shirt to reach maximum height is: 2.75 seconds

The maximum height reached is: 125 ft

Range of the function is: h = 4ft to 125 ft

The vertical motion equation for the ball is calculated using the formula:

h = h₀ + vt - ¹/₂gt²

where g = 32 ft/s²

v = 88 ft/s

h₀ = 4 ft

Thus, we have the equation as:

h = -¹/₂(32)t² + 88t + 4

h(t) = -16t² + 88t + 4

Now, the time it will take to reach maximum height is the value of t when the first derivative of the height equation is gotten and equated to zero. Thus:

h'(t) = -32t + 88

At h'(t) = 0, we have:

-32t + 88 = 0

32t = 88

t = 88/32

t = 2.75 seconds

The maximum height will be gotten by plugging in 2.75 s for t in the height equation to get:

h(2.75) = -16(2.75)² + 88(2.75) + 4

h(2.75) = 125 ft

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3 apple + 7 blackberrys = 99

2 apple + 14 blackberrys = 178

Then now find

apples = (99 - 7 B)/3 = (178 - 14B)/2

Now make cross multiply

(99 - 7B) •2 = (178 - 14B) •3

Solve parenthesis, use a (b+c) = ab + ac

Then

198 - 14B = 534 - 42B

Now find Blackberrys B PRICE

42B - 14B = 534 - 198

28B = 336

B= 336/28 = 12

Now find Apples price

Apples= ( 99 - 7B) /3 = (99 - 7•12)/3 = 15/3= 5

Then final answer is

Apple's price= $5

Blackberry's price= $12

Answer:

hhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

x=9

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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The simplifying value of the expression is,

⇒ \((875x^{5}y^{9} )^{1/3}\)

We have to given that,

An expression to solve,

⇒ 5xy³ ∛(7x²)

Now, We can simplifying it in Order the simplification steps as,

⇒ 5xy³ ∛(7x²)

⇒ \(5^{1} * 7^{1/3} * x^{1} *x^{2/3} * y^{3}\)

⇒ \((125 * 7)^{1/3} * x^{5/3} * y^{9/3}\)

⇒ \((875x^{5}y^{9} )^{1/3}\)

Thus, The simplifying value of the expression is,

⇒ \((875x^{5}y^{9} )^{1/3}\)

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The simplification steps of the expression (125)^3 ×7^1/3 × x^1 × x^2/3.

Simplification is the process a mathematical expression by an equivalent one, that is simpler.

Simplification steps of the expression:

\(5xy^3\sqrt[3]{7x^2} \\5xy^3.7^\frac{1}{3} x^\frac{2}{3} \\\)

5 = (125)^1/3

(125)^3 ×7^1/3 × x^1 × x^2/3.

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Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)