Researchers conducted a study to find out if there is a difference in the use of ereaders by different age groups. randomly selected participants were divided into two age groupsin the to 29year-old group7% of the 628 surveyed use ereaders, while 11of the 2,309 participants 30 years old and older use ereaders(use subscripts let 1 16- to 29-year-old users , and 230 years old and

The z-score for which 50% of the distribution's area lies between -z and z is 0, and the z-scores for which 25% of the distribution's area lies to the left of -z and to the right of z are -0.67 and 0.67,

The z-score for which 50% of the distribution's area lies between -z and z is 0.

The z-score measures the number of standard deviations a given value is away from the mean of the distribution.

When 50% of the distribution's area lies between -z and z, this means that the area under the normal curve between -z and z is equal to 0.50 or 50%.

Since the normal distribution is symmetrical around its mean, this also means that the area to the left of -z is 0.25 or 25% and the area to the right of z is also 0.25 or 25%.

We can use a standard normal table or a calculator to find the z-score for which the area to the left of it is 0.25. This z-score is -0.67.

Learn more about  Z-Score

brainly.com/question/15016913

#SPJ11

Looking at the given diagram,

angle 9x - 1 and angle y - 20 are linear pairs. they lie on a straight line. The sum of the angles on a straight line is 180 degrees. It means that

9x - 1 + y - 20 = 180

y = 180 + 1 + 20 - 9x

y = 201 - 9x equation 1

Also, angle 5x - 15 and angle y - 20 are vertically opposite angles. Vertically opposite angles are equal. It means that

5x - 15 = y - 20 equation 2

Substituting equation 1 into equation 2, it becomes

5x - 15 = 201 - 9x - 20

Collecting like terms, it becomes

5x + 9x = 201 - 20 + 15

14x = 196

x = 196/14

x = 14

y = 201 - 9x = 201 - 9 * 14

y = 201 - 126

y = 75+

Answer:

y = 3x + 1

Step-by-step explanation:

You have to use y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c  ⇒  y - intercept

First let us find the slope by using the below formula.

For that, let us use the given coordinates.

( -1 , -2 ) ⇒ ( x₁ , y₁ )

(-2 , -5)  ⇒  ( x₂ , y₂ )

m = \(\frac{y_1-y_2}{x_1-x_2}\)

m = \(\frac{-2-(-5)}{-1-(-2)}\)

m = \(\frac{-2+5}{-1+2}\)

m = \(\frac{3}{1}\)

m = 3

Now we have to find the y - intercept.

For that we can use any coordinate for that.

Let us use ( -1 , -2 ) coordinate.

y = m x + c

-2 = 3 × -1 + c

-2 = -3 + c

- 2 + 3 = c

1 = c

Let us write the equation of the line now.

y = m x + c

y = 3 x + 1

Let me know if you have any other questions. :-)

In the following question, A linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data is said to be True.

What is a linear system? In mathematics, a linear system refers to a system of linear equations that can be expressed in matrix form as Ax = b. A is a matrix, x is a vector, and b is a constant vector. When working with linear systems, we must keep track of the numerical accuracy of the computations. When a small change in the matrix or constant vector produces a large change in the solution, the matrix is said to be ill-conditioned.

The mathematical concept of condition numbers measures the sensitivity of a matrix to changes in the problem data. If a matrix has a high condition number, it is said to be ill-conditioned, whereas if it has a low condition number, it is said to be well-conditioned. An ill-conditioned matrix is difficult to solve numerically because a small error in the input data can produce a large error in the computed solution.

Therefore, the statement that "a linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data" is correct, and it is true.

For more such questions on linear system

https://brainly.com/question/2030026

#SPJ11


Answer:

the mean is 8 for x

8 = x + 2x / 2

16 = 3x

x = 16/3

x = 5.3

therefore the coordinate of x are ( 5.3,10.6)

for the y coordinate

-10= y +2y /2

-20 = 3y

y = -6.6

The coordinate of y are ( -6.6, - 13.3 )

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

Learn more about scale factor here: https://brainly.com/question/2826496

#SPJ1

Answer:

4y - x = 20

Step-by-step explanation:

Y= x/4 + 5/1

Cross multiply to get = y= (x+20/4)

4y = x+20

4y - x =20

Answer:

Step-by-step explanation:

1/8

Answer:

it is linear and proportional

Step-by-step explanation:

The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

To learn more about probability visit

https://brainly.com/question/12844710

#SPJ4

I donno is there anything else

The 150 kilometres per hour is the rate or speed of object.

The kilometres is indicative of distance and hour is indicative of time. So the fraction of kilometre and hour indicates the speed or rate of object. The rate or speed find wide applicability in calculations and can be indicative of multiple things.

For instance, the distance covered in an hour can signify the rate of descendence of bucket in the well, landing or flying of airplane, and other things. The same thing can also indicate speed in terms of distance travelled by any object like car, bus, airplane, protons, neutrons, atoms, gas molecules in an hour.

Learn more about rate -

https://brainly.com/question/25537936

#SPJ4

Answer:

the answer is C. 105°

Step-by-step explanation:

hope this helps

Let it's supplementary angle be x

So

\(\\ \sf\longmapsto 75+x=180\)

\(\\ \sf\longmapsto x=180-75\)

\(\\ \sf\longmapsto x=105°\)

Option C is correct

Answer:

2+n = 8

Step-by-step explanation:

2+ something must equal 8.

8 minus 2 = 6

n=6

Answer:

According to question,

2+ n =8

=) n = 8-2

=) n =6

hope you understand.

Answer:

Step-by-step explanation:

I think it should be 20 because the line is similar to the 18 line so you can round up to 20.

It aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.

Although the standard deviation is a frequently used statistic, it rarely receives the attention it merits. Although the mean and median are frequently mentioned in the news, they are rarely accompanied by any indication of how diverse the underlying data set was, so you only get a partial picture. In actuality, you might be overlooking the most captivating aspect of the tale.

What is Standard deviation?

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

To learn more about standard deviation from the given link

https://brainly.com/question/23907081

#SPJ1

Answer: To check if the rates form a proportion, we need to calculate the rate (sit-ups per minute) for both Eric and John.

Eric's rate: 70 sit-ups / 2 minutes = 35 sit-ups per minute

John's rate: 108 sit-ups / 3 minutes = 36 sit-ups per minute

Now we can set up the proportion:

35/1 = 36/1

The rates do not form a proportion since they are not equal.

Step-by-step explanation:

A sample size of 1500 or 10000 is generally sufficient for a reasonably accurate poll if proper methodology and random sampling techniques are utilized.

The correct answer is option A and B.

Determining a sufficient sample size for a reasonably accurate poll requires considering several factors: the population size, desired margin of error, confidence level, and expected variability within the population.

To calculate the sample size, we can use the formula:

n = (\(Z^2 * p * (1-p)) / (E^2)\)

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level

p = estimated proportion or expected prevalence in the population

E = desired margin of error

For example, let's assume we want a 95% confidence level, a margin of error of 5%, and an estimated prevalence of 50% (which provides the maximum required sample size). Plugging these values into the formula, we have:

Z = 1.96 (corresponding to a 95% confidence level)

E = 0.05 (5% margin of error)

p = 0.5 (estimated prevalence)

n = (\(1.96^2\) * 0.5 * (1-0.5)) / (0.05^2)

n = (3.8416 * 0.25) / 0.0025

n = 0.9604 / 0.0025

n = 384.16

Therefore, the required sample size would be approximately 384. This calculation assumes a worst-case scenario (p = 0.5) to ensure a conservative sample size estimate.

Based on the given options:

- A sample size of 1500 exceeds the required sample size, providing a reasonably accurate poll.

- A sample size of 10000 is more than sufficient and would yield an even more accurate poll.

- Sampling 10 percent of the population can be considered sufficient, depending on the total population size.

- Sampling 100 percent of the population would provide the most accurate results, but it is usually impractical or impossible.

In conclusion, both a sample size of 1500 and 10000 are correct answer making option A and B the correct answer.

For more such information on: sample size

https://brainly.com/question/28583871

#SPJ8

The question probable may be:

Which of the following sample sizes is sufficient to have a reasonably accurate poll? Group of answer choices:

A. 1500

B. 10000

C. 10 percent of the population

D. 100 percent of the population

Answer:

1

explanation in head

Answer:

k= 17

Step-by-step explanation:

51÷3 = k

k = 17

this is the answer

The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

Learn more about sampling technique here:

https://brainly.com/question/31697553

#SPJ11

Answer:

She drove about 16.67 miles per gallon.

Answer: 16.6 or 17 if we’re rounding

Step-by-step explanation:

Answer:

Step-by-step explanation:

The cosine function is: adjacent/hypotenuse = cos (40). We know the hypotenuse length is 10, so the equation is now adjacent/10 = cos (40). Solving for adjacent length we get 7.66 inches.

8.8x\(10^{24}\) formula units of \(MgCl_2\) are equal to 4.868 moles of \(MgCl_2\).

To determine the number of moles of \(MgCl_2\) in 8.8x\(10^{24}\) formula units, you need to use Avogadro's number, which is the number of particles (atoms, molecules, or formula units) in one mole of a substance. Avogadro's number is approximately 6.022 x \(10^{23}\) particles per mole.

The formula for \(MgCl_2\) contains one Mg atom and two Cl atoms, so one formula unit of \(MgCl_2\) contains three particles.

To find the number of moles of \(MgCl_2\), we can use the following formula:

moles = number of particles / Avogadro's number

First, we need to calculate the number of formula units of MgCl2:

8.8x\(10^{24}\) formula units of \(MgCl_2\) / 3 particles per formula unit = 2.933 x \(10^{24}\) particles

Next, we can calculate the number of moles:

moles = 2.933 x \(10^{24}\) particles / 6.022 x \(10^{23}\) particles/mole

moles = 4.868 moles.

Therefore, 8.8x\(10^{24}\) formula units of \(MgCl_2\) are equal to 4.868 moles of \(MgCl_2\).

Learn more about moles at

https://brainly.com/question/20486415

#SPJ4

(a) To construct a 95% confidence interval for the proportion of all customers who fill up their cup more than 3 times, we can use the formula:

CI = p ± z*√((p(1-p))/n)

where pis the sample proportion, z is the z-score corresponding to the confidence level (95% corresponds to a z-score of 1.96), and n is the sample size.

In this case, we have p= 19/90 = 0.2111. Plugging in the values, we get:

CI = 0.2111 ± 1.96*√((0.2111(1-0.2111))/90)

CI = (0.1084, 0.3138)

Interpreting this interval, we can say that we are 95% confident that the true proportion of all customers who fill up their cup more than 3 times when ordering a drink and eating in the restaurant falls between 10.84% and 31.38%.

(b) To calculate the minimum number of times a customer must fill up their cup for the restaurant to start losing money on the drink, we need to know the cost per drink and the profit margin on each drink. Let's assume that the cost per drink is $0.25 and the profit margin is 75% (i.e., the restaurant makes $0.75 for every $1.00 in sales).

If a customer fills up their cup more than 3 times, they are essentially getting more than 4 drinks for the price of one. So, if the cost per drink is $0.25 and the customer pays $1.00 for the drink, the restaurant is losing $0.75 for every extra drink that the customer gets. Therefore, the minimum number of times a customer must fill up their cup for the restaurant to start losing money is:

$1.00 ÷ $0.75 = 1.33

In other words, if a customer fills up their cup more than 1.33 times, the restaurant is losing money on the drink.

Visit here to learn more about confidence interval brainly.com/question/24131141
#SPJ11

Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 68° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

 From right angle triangle

     x = 16 × cos 68°

    x = 16 × 0.4067

    x = 6.5077

  x = 6.5 ft

The length of the ladder = 6.5 ft

By dividing the amount of white sugar by brown sugar we get, 2 2/3. The quotient is 2.

A fraction is a numerical quantity that is not a whole number. In other words, fraction can be defined as a small or tiny part, amount, or proportion of something.

A fraction represented with its quotient and remainder is a mixed fraction.  In other words, a mixed fraction is a combination of a whole number and a proper fraction.

Amount of white sugar  ÷ Amount of brown sugar

2/3 ÷ 1/4

2/3 × 4/1

8/3

2 2/3.

Here quotient is 2 and 2 is the remainder.

To learn more about fractions, visit :brainly.com/question/10354322

# SPJ9

h bvv    bv                                      

In cylindrical coordinates, the point (-9, 9, 9) is represented as (sqrt(162), π/4, 9), where r = sqrt(162), θ = π/4, and z = 9.

To change the point (-9, 9, 9) from rectangular coordinates to cylindrical coordinates, we need to determine the corresponding values of the radial distance (r), azimuthal angle (θ), and height (z).

The radial distance (r) can be found using the formula: \(r=\sqrt{x^2 + y^2}\)

In this case, x = -9 and y = 9: \(r= \sqrt{(-9)^2 + (9)^2} = \sqrt{81+81} = \sqrt{162}\)

The azimuthal angle (θ) can be found using the formula: θ = a tan2(y, x)

In this case, x = -9 and y = 9: θ = atan2(9, -9)

Since both x and y are positive, the angle θ will be in the first quadrant: θ = a tan2(9, -9) = π/4

The height (z) remains unchanged, which is 9 in this case.

Therefore, in cylindrical coordinates, the point (-9, 9, 9) is represented as (sqrt(162), π/4, 9), where r = sqrt(162), θ = π/4, and z = 9.

To know more about "azimuthal" refer here:

https://brainly.com/question/30663719#

#SPJ11

Answer:

the answer is $5 each

Step-by-step explanation:

30÷6=5