The position of a particle as a function of time is given by x=(6m/s)t+(−2m/s2)t2.A) Find the average velocity of the particle from t=0 to t=1s.B) Find the average speed from t=0 to t=1s.

50% of the adults consume less than 200 mg of caffeine daily.

We first must use the z-score formula, as follows:

\(Z = \frac{X - \mu}{\sigma}\)

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

\(\mu = 200, \sigma = 48\)

The proportion is the p-value of Z when X = 200, hence:

Z = (200 - 200)/48

Z = 0.

Z = 0 has a p-value of 0.5.

Hence the percentage is given as follows:

0.5 x 100% = 50%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ4

In total, Menaha traveled 97km 1000m (97.1km).

Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.

Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)

and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres

And the car distance is 11,480 metres.
When added together,

the total distance is 97,000 metres (97km).

To know more about distance click-
https://brainly.com/question/23848540
#SPJ4

Answer:

This is an enlargement.

Step-by-step explanation:

This is an enlargement.

A reduction would be smaller

A rotation would be changing the angle and a reflection would be a mirror image

The thermal resistance associated with the given wall is \(\(\frac{{25}}{{k \times 16.25}}\)\)

To calculate the thermal resistance of the wall, we can use the formula:

\(\[R = \frac{{\Delta x}}{{kA}}\]\)

where\(\(R\)\) is the thermal resistance, \(\(\Delta x\)\)  is the thickness of the wall, \(\(k\)\) is the thermal conductivity of the wall material, and \(\(A\)\) is the cross-sectional area of heat transfer.

Step 1: Calculate the thickness of the wall \((\(\Delta x\))\)

Since the wall consists of 10 studs, each with a height of 2.5 m, the total thickness of the wall is \(\(10 \times 2.5 \, \text{m} = 25 \, \text{m}\).\)

Step 2: Calculate the cross-sectional area \((\(A\))\):

The cross-sectional area of heat transfer is equal to the product of the height and width of the wall, given by  \(\(2.5 \, \text{m} \times 6.5 \, \text{m} = 16.25 \, \text{m}^2\).\)

Step 3: Obtain the thermal conductivity \((\(k\))\) of the wall material:

The thermal conductivity depends on the specific material used for the wall. Refer to the material's specifications or consult relevant sources to obtain the thermal conductivity value in units of\(\(\text{W/m} \cdot \text{K}\).\)

Step 4: Calculate the thermal resistance \((\(R\))\):

Substituting the values into the formula, we have:

\(\(R = \frac{{25 \, \text{m}}}{{k \times 16.25 \, \text{m}^2}}\).\)

Remember to replace \(\(k\)\) with the actual thermal conductivity value.

In summary, to calculate the thermal resistance of the wall, determine the thickness \((\(\Delta x\))\) , calculate the cross-sectional area\((\(A\))\), obtain the thermal conductivity \((\(k\))\), and substitute the values into the formula to obtain the thermal resistance \((\(R\)).\)

Learn more about thermal resistance from the given link: https://brainly.com/question/33495792

#SPJ11

answer:

D. y = 3x + 9

perpendicular means negative reciprocal of the number next to x

so if its 5x perpendicular would be -1/5x

make the equation look like y = ...

2x + 6y = 6

6y = -2x + 6

y = (-2x + 6)/6

y = -2x/6 + 6/6

y = -1/3x + 1

perpendicular line would be a negative reciprocal so

-1/3x would have a perpendicular that would be 3x

D. is the only one that has 3x

Because the sides are not raised correspondingly, PQRST is not an exact replica of ABCDE on a smaller size.

What is scaled copy?

If the same scale factor is applied to scaling each segment of the preimage or original image to determine the length of the corresponding segments of the scale copy or image, then one polygon is said to be a scaled copy of another polygon. All parts must be sized proportionally, in other words.

The numerous preimage segments of polygon PQRST, which is the new image of polygon ABCDE, are scaled using a variety of scale factors. Simply put, the sides of PQRST were not correspondingly increased. PQRST is not a scaled replica of ABCDE as a result.

To know more about the scaled copy, click on the link

https://brainly.com/question/17421952

#SPJ13

for every one (1) you have, you have 3 times the first

Ok,

for example for every 1 penny you have, you have 3dollars,

you counted and you have 4 pennies, in order to find out how many dollars you have, you have to times 4 by 3 to get 12

altogether you would have 4 pennies: 12 dollars.

\(\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}\)

Step-by-step explanation:

Matching of the equation will be:

A) x= -7

B) x= 3

C) x= 9

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

A) 3(x-5) = 2(x-11) has x= -7 as the solution.

B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.

C) 3(x+1) -2x = x+3 has x= 9 as the solution.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

To learn more about stratified sampling  Click Here:  brainly.com/question/30397570

#SPJ11

Answer:

6

Step-by-step explanation:

12 is the full length. point E marks 1/2 of the line. 12-6=6

if it's asking the length of d-e, then the answer is (6) because the entire length of line is twelve and in the top line e-f in 6 and 6-12=6

The correct options regarding given function  are (b), (c) and (f).

What is a function?

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function.

The set of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it gives as outputs.

The options given are:

a)The function f(x) = 9,000(\(1.05^{x}\)) represents the situation.

b)The function f(x) = 9,000(\(0.95^{x}\)) represents the situation.

c)After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.

d)After 4 years, the farmer can estimate that there will be about 1,800 bees remaining.

e)The domain values, in the context of the situation, are limited to whole numbers.

f)The range values, in the context of the situation, are limited to whole numbers.

Now given,

Number of bees initially = 9000

Rate of decay = 5%

f(x) = Number of bee population after x years

So, f(x) = 9000(\(0.95^{x}\))

After 2 years, number of bees is

  f(2) = 9000(0.95²) = 8122.5 ≈ 8120

After 4 years, number of bees is

 f(4) = 9000(0.95⁴) = 7330.56≈7330

The domain of the function is number of years(x) which can be whole as well as decimal numbers.

The range of the function is number of bees after x years, which should be a positive integer number. So whole numbers are the domain.

Therefore the correct options regarding given function  are (b), (c) and (f).

To learn more about function,follow the link.

https://brainly.com/question/25638609

#SPJ1

Answer:

Step-by-step explanation:

triangles PWR and AWB are equivalent (AAS/angle angle side)

RW and BW are equivalent (CPCT)

The scale factors are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Considering two equivalent side lengths, the scale factors are given as follows:

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To learn more about a vector as a linear combination of vectors using a system of equations from the given link

https://brainly.com/question/30758379

#SPJ4

The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Learn more about linear combination

https://brainly.com/question/32297475

#SPJ4

Answer:

4

Step-by-step explanation:

Answer:

m = 5

Step-by-step explanation:

to one side length of 4 to 2, we divided by 2 so why not divide 10 by 2

10 ÷ 2 = 5

Please give me brainliest!

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

To learn more about : radius

https://brainly.com/question/24375372

#SPJ11

Answer:

The ratio of original area to enlarged area is 1/4.

Step-by-step explanation:

Area of original circular garden is

\(\pi {( \frac{d}{2} )}^{2} = \pi \frac{ {d}^{2} }{4} \)

Area of enlarged circular garden is

\(\pi ( { \frac{2d}{2}) }^{2} = \pi {d}^{2} \)

So the ratio of original area to enlarged area is 1/4.

Answer:

Point Form:

(3 , 1 )

Equation Form:

x = 3 , y = 1

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

The general solution to the differential equation is y = [-(1/4)x^2 - (1/3)x + (C/4)]^(1/3).

To solve 2yy' + x^2 + y^2 + x = 0 using an appropriate substitution, we can substitute u = y^2. Taking the derivative of u with respect to x, we get du/dx = 2yy'. We can then rewrite the original equation as 2(u^(1/2))(du/dx) + x^2 + u + x = 0.

This is now a separable differential equation, where we can move the u term to the right side and the x terms to the left side: 2(u^(1/2))du/u = -(x^2 + x)dx. Integrating both sides, we get 4/3u^(3/2) = -(1/3)x^3 - 1/2x^2 + C, where C is the constant of integration.

Substituting back u = y^2, we get 4/3y^3 = -(1/3)x^3 - 1/2x^2 + C.

To know more about the differential equation, click here;

https://brainly.com/question/31492438

#SPJ11

If an ankle injury patient is willing to pay for both operation and inspection steps, Value-added time is less than 50% of cycle time

The ankle injury is under 1.5 times as much pressure with each stride .

In an avergae we travel 1000 miles on foot annully.

Over 14.2 million visits to doctors is due to ankle injuries every year.

However only 15% of the total injuries results in fractures.

Therefore, if an ankle injury patient is willing to pay for both operation and inspection steps, the statements which is true is Value-added time is less than 50% of cycle time

To learn more about chart refer here

https://brainly.com/question/28032677

#SPJ4

Answer:

Step-by-step explanation:

affffF

f

ef

s

fse

s

fse

fse

f

fs

f

wsf

s

fs

fs

f

s

fs

fs

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

Answer:

15%

Step-by-step explanation:

8 out of 52 = 15%

Hope this helps! :)

The $10 scale is a good scale to use for the y-axis. 12 months is sufficient to plot the graph and display the changes.

What is a coordinate system?

coordinate system, Setup of reference lines or curves that are used to pinpoint the locations of points in space The most popular two-dimensional system is called Cartesian (after René Descartes). Points are identified by their separation from a reference point, known as the origin, along a horizontal (x) and vertical (y) axis (0, 0).

Let the y-axis represent the money for groceries and the x-axis the number of months.

Given is that, the grocery bills range from $110 to $170.

We can thus view the changes in the grocery bills over 7 intervals by placing a scale of $10 on the y-axis.

Consequently, a $10 scale is a good scale.

Additionally, the y-axis shows the number of months. It will be sufficient to plot the graph and display the changes in grocery bills over the course of 12 months.

Therefore, 12 points are enough to represent a month.

To know more about the coordinate system here:

https://brainly.com/question/4726772

#SPJ4

The mean and standard deviation of a binomial distribution with n = 900 and p = 1/3 can be determined as follows:

Mean = n * p = 900 * (1/3) = 300

Standard Deviation = √(n * p * (1 - p)) = √(900 * (1/3) * (2/3)) ≈ 14.14

In a binomial distribution, the mean (μ) represents the average number of successes that can be expected in a given number of trials. It is calculated by multiplying the number of trials (n) by the probability of success (p). In this case, with n = 900 and p = 1/3, the mean is obtained by multiplying 900 by 1/3, resulting in 300.

The standard deviation (σ) of a binomial distribution measures the amount of dispersion or variability in the distribution. It is calculated using the formula √(n * p * (1 - p)). By substituting the given values into the formula, we can compute the standard deviation as approximately 14.14.

Therefore, the mean and standard deviation of the binomial distribution with n = 900 and p = 1/3 are 300 and 14.14, respectively.

Learn more about:Bionomial distribution

brainly.com/question/14565246

#SPJ11

Answer:

x ≥ 3

Step-by-step explanation:

the domain of a graph consists of all the input values shown on the x -axis

The domain of the square root function graphed below would be x ≥ 3

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable , functions are indispensable for formulating physical relationships.

The domain is all  real numbers for x>3 and the range of the square root function graphed is equal to the interval------> [1,∞)

so, the range is all real numbers for x>3

Hence, the domain of a graph consists of all the input values of the x -axis.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ7

Answer:

51

Step-by-step explanation:

4(9+4)-6(9+2)

9(13)-6(11)

117-66

51

Answer:

the answer for 4(9 + 4) – 6(9+2) is 54