the distribution of the heights of five-year-old children has a mean of 42.5 inches. a pediatrician believes the five-year-old children in a city are taller on average. the pediatrician selects a random sample of 40 five-year-old children and measures their heights. the mean height of the sample is 44.1 inches with a standard deviation of 3.5 inches. do the data provide convincing evidence at the level that the mean height of five-year-old children in this city is greater than 42.5 inches?

It is difficult to estimate the exact number of smartphones in the group and the standard deviation, as this depends on what type of smartphones each person has. It could take between 1 and 8 people to find a smartphone, depending on the number of smartphones already in the group.

The number of smartphones in the group of 8 people is difficult to estimate, as it depends on the type of smartphone each person has. For example, if there are 2 people with iPhones, 3 people with Android phones, and 3 people with Windows phones, then there would be 8 smartphones in the group. However, if there is only one person with an iPhone and the other 7 have different types of phones, then there would be only 4 smartphones in the group. The standard deviation of the number of smartphones in the group would depend on how many different types of smartphones are present and the total number of smartphones in the group. The amount of time it would take to find a smartphone would depend on the number of smartphones already in the group. If there are already 4 or more smartphones, then it would take only 1 person to find a smartphone. If there are only 3 smartphones, then it could take up to 8 people before one of them has a smartphone.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

Answer:

0.27

Step-by-step explanation:

I hope this helps :)

The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.

The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y

Let us simplify the left hand side (LHS) :

Make the denominator same to (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))

y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)

y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)

Now plugging this simplified version in LHS

(y² + 16)/ (y² - 16) = 32/ y

y(y² + 16) = 32(y² - 16)

y³ - 32y² + 16y + 32×16 = 0

The solutions are approximately 30.948, 4.627 and -3.575.

To know more on cubic polynomial

https://brainly.com/question/1417425

#SPJ4

To find the domain and range of a system of inequalities, you need to solve the system of inequalities, plot the solution, determine inequality sign for solution, shade area of solution, then the x-values of the area represent domain and y values represent range.

Solve the system of inequalities for x and y in terms of each other.

Plot the solutions on a coordinate plane. Each solution will be a boundary line for the solution set.

Determine the inequality signs for each solution. Solutions with < or > signs will be represented as a dashed line, while solutions with ≤ or ≥ signs will be represented as a solid line.

Shade the portion of the coordinate plane that satisfies all of the inequalities.

The shaded area represents the solution set for the system of inequalities.

The domain is the set of all x-values that are included in the solution set and the range is the set of all y-values that are included in the solution set.

To know more on domain and range

https://brainly.com/question/28135761

#SPJ4

So the Statement the first step in the K-means clustering algorithm is to randomly assign each observation within the data set to a cluster from 1 to k.

Hence, The first step in the K-means clustering algorithm is to randomly assign each observation within the data set to a cluster from 1 to k.

K-means cluster algorithm:

K-Means Clustering is an unsupervised learning algorithm that is used to solve clustering problems in machine learning or data science. In this topic, we will learn what is K-means clustering algorithm is, how the algorithm works, along with the Python implementation of k-means clustering.

The first step in the K-means clustering algorithm is to randomly assign each observation within the data set to one of the k clusters. This initial assignment is done randomly in order to ensure that the algorithm is not influenced by any initial ordering of the observations. The subsequent steps of the algorithm involve iteratively re-assigning observations to clusters and updating the cluster centroids until convergence is reached.

As a result, the K-means clustering algorithm's first step is to randomly assign each observation inside the data set to one of the k clusters, ranging from 1 to k.

To learn more about cluster algorithms, refer to the link: brainly.com/question/28178791

#SPJ4

Answer:

yes to all 3

Step-by-step explanation:

A

3z = 21 ( isolate z by dividing both sides by 3 )

z = 7

B

n + 14 = 36 ( subtract 14 from both sides )

n = 22

C

[tex]\frac{3}{4}[/tex] v = 12 ( multiply both sides by 4 to clear the fraction )

3v = 48 ( divide both sides by 3 )

v = 16

Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope[/tex]

(8,3)=(x1,y1)

(10,3)=(x2, y2)

Now,

[tex]m = \frac{3 - 3}{10 - 8} \\ = 0[/tex]

if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but the probability that such a coin will come up heads exactly half the time in 16 tosses is 1 in 65536 (2^16).

This can be calculated using the binomial probability formula which states that the probability of getting a certain number of heads in a certain number of tosses is given by (Number of ways to get the desired number of heads) / (Total number of possible outcomes). In this case, the number of ways to get 8 heads in 16 tosses is equal to 16C8, or 120.

The total number of possible outcomes is equal to 2^16, or 65536. Thus, the probability of getting 8 heads in 16 tosses is 120/65536, which is approximately equal to 1/65536.

To know more about the probability refer to the  link   brainly.com/question/30034780

#SPJ4

As per the unitary method, the original price of the watch is 217.11

The term unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have given that the price of a watch was decreased by 35% and sold for $75. 99.

Let us consider that x be the original price of watch.

Here we have given that the amount of discount is calculated as,

=> 35% of x = 75.99

=> 35/100 of x = 75.99

When we simplify this then we get,

=> 0.35 of x = 75.99

Then the value of x is calculated as,

=> x = 75.99/0.35

=> x = 217.11

Therefore, the correct option is (D).

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

The main difference between an equation and an inequality is in an equation the elements are equal but in an inequality the elements are compared.

A relationship between two expressions or values that are not equal to each other is called inequality.

An equation has an answer that equals a number. An inequality has an answer that could be less than or more than or less than or equal to or more than or equal to.

For example:  You have some money in your pocket. You want to buy some snacks for tonight's match, but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :

y ≤ x - 10     where x represents money in your pocket.

This means that from money in your pocket you have to subtract $10 for pizza and out of the remaining money you can spend some part of it on snacks or all of it.

Lean more about inequality, click;

https://brainly.com/question/30231190

#SPJ1

The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 97 cm and a standard deviation of 1 cm, and they are regularly distributed. 15 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.

mean is N (M) (109,1.6)

Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation

P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.

To learn more about Probability refer to:

brainly.com/question/28021875

#SPJ4

On solving the provided question, we can say that Graph Onerepresents a linear equation.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

Graph One

The graph is linear, commonly known as being in a straight line. Other graphs are not, though. Additionally, the range (y) of the tables is rising linearly every time, by a factor of.5 (1/2).

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ4

Answer:

A.) (0,5)

B.) -3/2

C.) y= (-3/2)x + 5

Step-by-step explanation:

A.) The y-intercept of a graph is the point where the function crosses the y-intercept. For the function shown in the graph, the y-intercept would be (0,5) or y=5.

B.) Slope can be determined by using rise over run. To determine the rise and run, we will need to look at 2 points. Let's use the points (0,5) and (2,2). Instead of "rising" from (0,5) to (2,2), we must "sink" 3, giving us a rise of -3. Next, to get from (0,5) to (2,2), we must "run to the right 2. So, our "rise over run" or "rise/run" would be -3/2. This means our slope is -3/2.

C.) When writing an equation for the line, we are going to want to write it in slope-intercept form. Slope-intercept form is often shown as y=mx+b, when m is the slope and b is the y-intercept. Since we know both the slope and y-intercept, we can plug those values into the slope-intercept form equation. This then changes y=mx+b into y=(-3/2)x+5.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

y= -3/2x+6

Point of intersection: (0,6)

Y Intercept: 6

Slope: -3/2

You can check slope by counting the number of units it goes down and to the side. it is rise/run so the amount of y values it goes down and x values goes to the side is the denominator.

Slope: rise/run= y1-y2/x2-x1

Step-by-step explanation:

The correct dotplot for the given data is option D, which displays the number of errors for the week for each workstation.

Error in math is any mistake made in the process of solving a mathematical problem or problem-solving process. It could mean a mistake in the calculations, incorrect steps taken, or incorrect assumptions made. It can also include making a wrong interpretation of the problem, or not being able to solve it at all. Errors in math can occur due to a lack of understanding of the concepts, mistakes in calculations, errors in reasoning, or incorrect application of the rules and formulas. Errors can also be made in the process of writing down the equations, or in the process of simplifying the equation.

The graph begins with 0 and goes up to 254201 in intervals of 5. The data points for each work station are marked on the graph, showing the number of errors each work station made. This visual display of data points allows for an easy comparison of the number of errors across all workstations.

To know more about error click-
https://brainly.com/question/28001423
#SPJ4

Stratified sampling is used when the population is heterogeneous.

What is Stratified sampling?

A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub-populations) and random samples are drawn from each. This increases representativeness as a proportion of each population is represented.

The sampling method described in the study is a stratified sampling method.

In stratified sampling, the population is first divided into subgroups or strata based on some relevant characteristic, such as size in this case.

Then, a simple random sample is taken from each stratum.

In this study, the sample is chosen by separating all cars by size and selecting 10 of each size grouping, this is the definition of stratified sampling.

Stratified sampling is useful when the population is heterogeneous and you want to ensure that the sample is representative of specific subgroups within the population.

This method allows for a more precise estimation of population characteristics and can reduce sampling error.

Hence, Stratified sampling is used when the population is heterogeneous.

To learn more about Stratified sampling visit,

https://brainly.com/question/20544692

#SPJ4

Answer:

  a ≠ 0

Step-by-step explanation:

You want to know the restriction applicable to 2(y+a)/a(x-3).

A rational expression is undefined when its denominator is zero. The restrictions are applied so that no denominator is zero.

Here, the expression is ...

  [tex]\dfrac{2(y+a)}{a}(x-3)[/tex]

The only denominator is 'a'. It cannot be zero.

The restriction is a ≠ 0.

__

Additional comment

If we assume this is a relation in which x- and y- are the only variables, there is no restriction on the relation as written.

Perhaps you intend that (x-3) be a denominator factor. Then the relation would have the restriction x≠3. Such an expression would need to be written as ...

  2(y+a)/(a(x-3)) . . . . . . using parentheses around the denominator

<95141404393>

Answer:

47

Step-by-step explanation:

Leading coefficient: 23

Degree: 8 (The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable "u" is 8, so the degree of the polynomial is 8.)

Answer:

i) 23

ii) 8

Step-by-step explanation:

i) leading coefficient:

23

ii) Degree

The degree of the polynomial is the highest power in the polynomial.

So,

degree of polynomial=8

The inverse function of y = 2(x - 5)² is  [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Let, y = 2(x - 5)².

y/2 = (x - 5)².

Solving for 'x'.

[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].

[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]

Now, We have to interchange the positions of x and y.

[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

learn more about inverse functions here :

https://brainly.com/question/2541698

#SPJ1

T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.

n = number of floor of the Princess Tower (Floor Number)

T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor

Tenant means a person occupying a rented land or property (A resident for simple understanding)

Therefore:

The statement:  T(60) > T(10) + T(30)

Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.

Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5

Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15

Learn more about mean here: brainly.com/question/19243813

#SPJ1

If Angel is trying to find the height of a radio antenna on the roof of a local building. The height of the antenna (the distance from point A to point B) is 8m.

Given data:

Horizontal distance = 18 meters

Angle of elevation from his eyes to the roof (point A) = 21°

Angle of elevation from his eyes to the top of the antenna (point B) = 39°

So,

AB= 18 × (Tan 39° - Tan 21°)

AB = 18 × ( 0.8098 - 0.3839)

AB = 18 × 0.4259

AB = 7.67

AB = 8m (Approximately)

Therefore the height of the antenna (the distance from point A to point B) is 8m.

Learn more about height here:https://brainly.com/question/1739912

#SPJ1

Answer: Since he is in school for 5 days a week, in a school week he will have a balance of 25.

Step-by-step explanation:

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

Let the number of green marbles be 'g'.

The probability of selecting a red marble before the number of green marbles is doubled is[tex]$\frac{4}{g+4} * 100 = x\%$[/tex]

The probability of selecting one of the four red marbles from the box after the number of green marbles is doubled is [tex]$\frac{4}{2g+4} * 100 = (x - 15)\%$[/tex]

Rearranging the equations and solving for g, we get:

[tex]\frac{4}{g+4} * 100 = x$\frac{4}{2g+4} * 100 = (x - 15)$$2g+4 = \frac{4}{x-15}$$g = \frac{4 - 4x + 60}{2x - 30}$[/tex]

Therefore, the number of green marbles before the number of green marbles is doubled is [tex]$\frac{4 - 4x + 60}{2x - 30}[/tex]

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

The experimental probability of a cube tossed 60 times, landing on a number greater than 4 is the option;

18 over 60

A probability is the fraction or proportion of the times an event will occur when an experiment or task is repeated. It is the measure of the liklyhood an event will occur

Probability compares the number of times an event occurs to the number of times all possible event outcomes occurs.

The formula for the experimental probability is presented as follows;

[tex]Probability = \frac{The \ sum \ of \ the \ times \ the \ event \ takes \ place}{The \ sum \ of \ the \ trials}[/tex]

The number of times the outcome from tossing the coin is greater than 4 obtained by adding the frequencies when for the outcomes of 5 and 6 are;

Number of outcomes greater than 4 = 10 + 8 = 18

The sum of all trials = 12 + 13 + 11 + 6 + 10 + 8 = 80

Therefore, the experimental probability = 18/60

The correct option is; 18 over 60

Learn more about experimental probability here: https://brainly.com/question/1275164

#SPJ1

Answer: B: 18/60 (18 over 60)

Step-by-step explanation:

On solving the provided question, we can say that the equation representing the path of each kangaroo. x = 4ft and y = 11ft

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation

let X be kangaroo 1

and Y be kangaroo 2.

So the equation

X = 3ft + 1ft

while

Y = 5ft + 1ft +.5ft.

and now,

x = 4ft and y = 11ft

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

Answer:

The measure of the third angle of the triangle is 45°.

Step-by-step explanation:

What is a triangle?

A triangle is a polygon with 3 sides.

Given that, the measures of the two angles of a triangle are 50° and 85°.

Let the measure of the third angle be x.

Since the sum of the interior of a triangle is 180°, it follows,

50°+85°+x=180°

135° +x = 180°

x = 180° - 135°

x = 45°

Hence, the measure of the third angle of the triangle is 45°.

Answer:

y^2 + 5y - 750 = 0

y(y + 5) = 750

750 - y(y - 5) = 0

Step-by-step explanation:

Simplification of the exponential expressions using laws of exponents gives;

A) 1

B)  ¹/₂

C) 2

D) 2

Some of the laws of exponents states that;

1) When we multiply like bases, we must keep the base the same and add the exponents.

2) When we raise a base with a power to another power, we must keep the base the same and multiply the exponents.

3) When dividing like bases, we must keep the base the same and subtract the denominator exponent from the numerator exponent.

A) [(2 * 3⁻²)³(5 * 3²)²]/(3⁻²)(5 * 2)²

Applying laws of exponents, we have;

[(2² * 3⁻²*³)(5² * 3²*²)]/(3⁻²)(5² * 2²)

= 2² and 5² will cancel out to give;

3⁻⁶ * 3⁴ * 3²

= 3⁻⁶ * 3⁴⁺²

= 3⁻⁶ * 3⁶

= 3⁰ = 1

B) (3³) (4⁰)²(3 * 2)⁻³ (2²)

This can be broken down into;

3³ * 1 * 3⁻³ * 2⁻³ * 2²

= 2⁻¹ = ¹/₂

C) (3⁷ * 4⁷)(2 * 5)⁻³(5²)]/(12⁷ * 5⁻¹ * 2⁻⁴)

= (3⁷ * 4⁷)(2⁻³ * 5⁻¹)/((3⁷ * 4⁷ * 5⁻¹ * 2⁻⁴)

3⁷ * 4⁷ * 5⁻¹ will cancel out to get;

2⁻³/2⁻⁴ = 2

D) ((2 * 3⁻¹) * 2⁰)/(2 * 3⁻¹)

(2 * 3⁻¹) will cancel out to get;

2⁰ = 1

Read more about Laws of Exponents at; https://brainly.com/question/11761858

#SPJ1