Five-year-old students at an elementary school were given a 30-yard head start in a race. The graph shows how far the avera

A line graph with Distance, in yards, on the x axis and Age of Runner on the y axis. The x axis has a scale from 0 to 80 in increments of 10. The y axis has a scale of 0 to 6 in increments of 2. A straight line connecting 30, 5 and 60, 5 is drawn.


Which statement best describes the domain of the function represented in the graph?
A. 5 ≤ x ≤ 60, or x is from 5 to 60
B. 5 ≤ x ≤ 30, or x is from 5 to 30
C. 30 ≤ x ≤ 60, or x is from 30 to 60
D. 0 ≤ x ≤ 30, or x is from 0 to 30

We know that the store discounts 30% of the original price for an item, then, to calculate the discount we just have to multiply the original sell price by the discount percent and divide it by 100, like this:

Then, the discount is $109.5.

The new total would be the difference between the original price of the item and the discount, like this:

New price= $365-$109.5=$255.5

The correct answer to the exponential expression which is as given in the task content is; 8³.

Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.

Gina's working:

8^12 / 8^9

= 0^12 / 0^9

The Correct workings:

8^12 / 8^9

= 8^(12-9)

= 8³

So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.

Learn more about exponent:

https://brainly.com/question/11975096

#SPJ1

The appropriate family of distributions to approximate the probability of rolling a 6 on a fair die is the discrete uniform distribution, which assumes equal probabilities for each outcome. In this case, the probability of rolling a 6 would be approximately 1/6 based on the assumption of fairness.

For the problem of approximating the probability of rolling a 6 on a fair die, an appropriate family of distributions to consider is the discrete uniform distribution.

The discrete uniform distribution is commonly used to model situations where each outcome has an equal probability of occurring. In the case of rolling a fair die, the die has six equally likely outcomes (numbers 1 to 6).

Each outcome has a probability of 1/6 of occurring, making the discrete uniform distribution a suitable choice.

By assuming a discrete uniform distribution, we can assign equal probabilities to each outcome (1/6 for rolling a 6) and approximate the probability of rolling a 6 based on the assumption of fairness.

To know more about discrete uniform distribution refer here:

https://brainly.com/question/31603031#

#SPJ11

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

Given data:

X: height of seaweed.

       X~N (μ;σ²)

       μ= 10 cm

       σ= 2 cm

We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

              P(X ≤ x) = 0.30

              P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

        Z = (X - μ)/σ

translates the Z value to the corresponding X value.

           P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                  z= -0.52

Now you have to clear the value of X:

        Z= (X - μ)/σ

        X= (Z * σ) + μ

       X = (-0.52 * 2) + 10

         = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

To learn more about normal distribution, visit:

brainly.com/question/23418254

#SPJ4

The rows selected for the predicate "enrol_mark >= 50" by the DBMS will include all rows where the value of the column "enrol_mark" is greater than or equal to 50.

In a DBMS (Database Management System), a predicate is a condition or criteria used to filter and select specific rows from a database table. In this case, the predicate "enrol_mark >= 50" indicates that we are interested in selecting rows where the value of the "enrol_mark" column is greater than or equal to 50.

When the DBMS evaluates this predicate, it will scan the table and compare the value of the "enrol_mark" column for each row. If the value is greater than or equal to 50, the row will be selected and included in the result set. Rows with "enrol_mark" values less than 50 will not be included in the result set.

It's important to note that the actual rows selected by the DBMS will depend on the specific data in the table. If there are rows where the "enrol_mark" column has values greater than or equal to 50, those rows will be selected. If there are no such rows, then the result set will be empty.

Learn more about data here:
brainly.com/question/28285882

#SPJ11

For  -5 + 3.25, we will start from -5 and move to the right by 3.25 units as shown to have 1.75

Similarly for 3.18+(-7), we will start from 3.18 and move to the left by 7 units as shown to have -3.82

For the expression -5 + 3.25

The number line contains both negative and positive values. negative numbers are to the left of the line while positive values are to the right of the line

For  -5 + 3.25, we will start from -5 and move to the right by 3.25 units as shown to have 1.75

Similarly for 3.18+(-7), we will start from 3.18 and move to the left by 7 units as shown to have -3.82

Learn more here: https://brainly.com/question/15816805

Answer: From least to greatest: -2.4, -0.8, 0.2, 0.9, 1.6. Hope this helps you! :D

Answer:

-2.4,-0.8,0.2,0.9,1.6

Step-by-step explanation:

in subtraction when there is minus sign, so the grater number will be smaller.

Answer:

If f'(x)= (x-1)^2(x+4), then the function y=f(x) has: (C) one local minimum and one local maximum.

To determine the local minimums and maximums of y=f(x), we need to find the critical points where f'(x)=0 or where f'(x) does not exist.

In this case, f'(x)= (x-1)^2(x+4), which equals zero at x=1 and has a vertical tangent at x=-4.

To determine the behavior of the function around these critical points, we can use the first derivative test.

- At x=1, f'(x) changes from negative to positive, indicating that the function has a local minimum at x=1.
- At x=-4, f'(x) is negative on both sides, indicating that the function has a local maximum at x=-4.

Therefore, the answer is (C) one local minimum and one local maximum.

To learn more about tangent, refer below:

https://brainly.com/question/19064965

#SPJ11

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

[1] y = 2x

- the line goes through the origin (0, 0) so there will be no b value

- the line, starting from (0, 0) goes up two and to the right 1 into the next point giving us a slope of 2/1 which simplifies to 2

[2] (0, 5)

- we can figure this out without graphing or plugging in values because (0, y) will be the y-intercept, or the b value

- in this case the value is 5

[3] y = 3x + 12

- it uses a different term than I am used too, but by "graident" I think they mean the slope

- if it has the same slope, then it will be a slope of 3

- if it passes through (0, 12) then again, this is the y-intercept or our b-value

Have a nice day!

-> See attached for more information on b values

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

The answer would be C, (The measure of ZY is the greatest of the three angles.)

YX=3, ZY=5, ZX= 4

(YX)≤(ZX)≤(ZY)

or

3≤4≤5

Answer:

A)  The measure of ∠X is the greatest of the three angles.

Step-by-step explanation:

In a triangle:

Therefore, in triangle XYZ, where XY = 3, YZ = 5 and XZ = 4:

The measure of the all the angles cannot be the same since the three side lengths are different.

Answer:

a.$1230

b.$20.50

Step-by-step explanation:

Assuming Landon only makes the minimum payments for the sixty months this is how you would find it

Multiply loan by percentage over the five years: 4100 x .3 = 1230

Then divide that amount by months paid: 1230/60= 20.5

The number 7 emerged in human history through cultural and mathematical developments.

The significance of the number 7 can be observed in various aspects of human history. One of the earliest instances is found in ancient Mesopotamia, where the Sumerians developed a base-60 numeral system called sexagesimal.

This system contributed to the use of 60 as a highly divisible number and influenced the concept of dividing the day into 24 hours, each consisting of 60 minutes.

In ancient Egypt, the division of the week into seven days was based on the observation of celestial bodies.

The Egyptians associated each day with a different planet or celestial object, namely Sunday (Sun), Monday (Moon), Tuesday (Mars), Wednesday (Mercury), Thursday (Jupiter), Friday (Venus), and Saturday (Saturn). These planetary associations were later adopted by the Romans, and their names in English still reflect these origins.

The number 7 also holds religious and symbolic significance. In Judaism, the seventh day of the week, Saturday, is considered a day of rest, known as the Sabbath.

This tradition is rooted in the biblical story of creation, where God rested on the seventh day. In Christianity, the Book of Genesis describes the world being created in six days, with the seventh day being designated as holy.

Furthermore, the number 7 appears in mathematics and geometry. The seven colors of the rainbow, the seven musical notes, and the seven wonders of the ancient world are all examples of the cultural significance attributed to this number.

Learn more about human history

brainly.com/question/1827651

#SPJ11

Answer:

46/10 or 23/5

Step-by-step explanation:

Answer:

46/10

Step-by-step explanation:

I got it right on imagine math

Answer:

Step-by-step explanation:

so you are trying to find the scale of the map which means you are comparing the distance on the map to the distance in real life. That being said you are trying to find:

For every 1cm on the map how far is that in real life?

so when you make your equation to solve like so (converting the miles to cm for an easy calculation:

2.5x = 48203

in this equation x (your answer) is the scale of map:real life

so x is how far 1cm on the map is in real life

Answer:

B

Step-by-step explanation:

{x+y=-1

3x-y=5}

(Sum)

x+y+3x-y=-1+5

4x=4

x=1

if x=1 then according to the first equation 1+y=-1 so:

y=-2

Answer:

Value of tan( π/3 ):

\({ \tt{ \frac{\pi}{3} = \frac{180}{3} = 60 \degree }}\)

60° lies within the first quadrant.

\({ \sf{ \tan( \frac{ \pi}{3} ) = ( \frac{1}{2} , \: \frac{ \sqrt{3} }{2}) }}\)

Since it's a half:

\({ \boxed{ \sf{ \tan( \frac{\pi}{3} ) = \sqrt{3} }}}\)

Length of hypotenuse:

\({ \bf{ \sin(31 \degree) = \frac{16.5}{h} }} \\ { \sf{h = 32.04}}\)

Hypotenuse = 32.0

Yes that is true the commutative does not hold for division.

Answer:

16

Step-by-step explanation:

(fog)x=f{g(x)}

=f(x-2)

=(x-2)^2

So,

(fog)(-2)=(-2-2)^2

=-4^2

=16

The change in Jane's total pay for each copy of "History is Fun" she sells is $70, and if she doesn't sell any copies, her total pay is $2200.

1. What is the change in Jane's total pay for each copy of "History is Fun" she sells?

According to the equation given, y = 2200 + 70x, the coefficient of 'x' is 70. This means that for every additional copy of "History is Fun" that Jane sells, her total pay increases by $70. Therefore, the change in Jane's total pay for each copy sold is $70 (positive).

2. What is Jane's total pay if she doesn't sell any copies of "History is Fun"?

If Jane doesn't sell any copies of "History is Fun," the equation y = 2200 + 70x helps us calculate her total pay. By substituting x = 0 into the equation, we find:

y = 2200 + 70(0)

y = 2200 + 0

y = 2200

Thus, if Jane doesn't sell any copies of "History is Fun," her total pay would still be $2200.

learn more about pay

brainly.com/question/3478684

#SPJ11

Answer:

-32 I THINK

Step-by-step explanation:

The y-intercept of the line passing through the given points is -5/2.

An intercept is a point on the y-axis, through which the slope of the line passes.

Given that, a line that passes through the point (1,-7) and (5, -25)

The equation of a line passing through two points is given by,

y-y1 = (y2-y1)/(x2-x1)(x-x1)

y+7 = -18/4(x-1)

y+7 = -9/2x+9/2

y = -9/2x+9/2-7

y = -9/2x-5/2

Hence, The y-intercept of the line passing through the given points is -5/2.

For more references on y intercept, click;

https://brainly.com/question/14180189

#SPJ2

The Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated. The Publicity Test indicates that the decision has been well received and is aligned with public expectations.

- The Publicity Test is designed to assess whether the decision or action can withstand public scrutiny and be disclosed openly.

- I score this test an 8 because the decision or action in question has already been made public and received positive feedback from various stakeholders.

- The organization has been transparent in its communication, engaging with the public and addressing concerns promptly.

- The decision aligns with the organization's values and mission, which resonates positively with the public.

- The organization has effectively managed any potential negative publicity by proactively addressing criticisms and providing clear justifications for the decision.

- Overall, the Publicity Test indicates that the decision has been well received and is aligned with public expectations.

The Moral Mentor Test Score: 6

- The Moral Mentor Test evaluates the decision or action by considering whether it reflects the guidance of a wise and ethical mentor.

- I score this test a 6 because while the decision is generally ethical, there are some potential ethical dilemmas that need to be carefully addressed.

- The decision has considered the welfare of various stakeholders and adheres to legal and regulatory frameworks.

- However, there might be some moral complexities associated with certain aspects of the decision that need further evaluation.

- It is important for the organization to seek guidance from ethical experts and consider potential long-term consequences to ensure the decision aligns with the principles of a moral mentor.

- Overall, the Moral Mentor Test suggests that the decision is on the right track but requires careful ethical analysis and considerations.

The Admired Observer Test Score: 9

- The Admired Observer Test assesses whether the decision or action would be approved by an admired and objective observer.

- I score this test a 9 because the decision demonstrates a high level of integrity and is likely to be approved by an objective observer.

- The decision is aligned with industry best practices and follows ethical guidelines.

- It takes into account the interests of various stakeholders and aims to maximize positive outcomes for all parties involved.

- The decision is well-reasoned, considering both short-term and long-term implications.

- Overall, the Admired Observer Test indicates that the decision is commendable and likely to be seen as fair and ethical by an objective observer.

The Transparency Test Score: 7

- The Transparency Test evaluates whether the decision-making process is transparent and accountable.

- I score this test a 7 because while the decision-making process has been relatively transparent, there is room for improvement.

- The organization has provided some level of information and rationale behind the decision, but there may be areas where more transparency is required.

- It is essential for the organization to proactively communicate the decision, its underlying factors, and potential impacts to ensure stakeholders have a clear understanding.

- Increasing transparency can help build trust and mitigate any potential misunderstandings or mistrust.

- The Person in the Mirror Test assesses whether the decision or action aligns with the individual's values and principles.

- I score this test an 8 because the decision demonstrates alignment with the individual's values and principles.

- The decision-maker has considered the ethical implications and personal integrity while making the decision.

- The decision reflects a commitment to fairness, honesty, and accountability.

I score this test a 9 because the decision demonstrates a high level of empathy and fairness towards others.

- The decision considers the interests and well-being of various stakeholders, treating them with respect and dignity.

- It reflects a commitment to fairness, equality, and reciprocity in relationships.

- The organization has taken steps to ensure that the decision does not cause harm or disproportionately benefit any specific group.

- Overall, the Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated.

Learn more about empathy here

https://brainly.com/question/20047598

#SPJ11

For the entire independent-measures experiment 24 individuals are participated.

Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.

We are given the value  t(22) = 5.30, p < .01

So here degree of freedom (df) is 22 and it is independent so there is two samples,

so df= n₁+n₂-2

⇒ 22 =  n₁+n₂-2

⇒ n₁+n₂ = 24.

Thus for the entire experiment 24 individuals are participated.

To learn more about independent-measures experiment, click here:

https://brainly.com/question/17699654

#SPJ4

The angle labelled ? is calculated using the sum of angles in a straight line to be 85 degrees

The sum of angles in a straight line is 180 degrees

starting from the straight line by the left, let the required will be x in each case

115 + x = 180

x = 180 - 115

x = 65 degrees

solving for the angles in the triangle

65 + 85 + y = 180

y = 180 - 65 - 85

y = 30 degrees

30 + 90 + z = 180   (angles on a straight line)

z = 180 - 90 - 30

z = 60 degrees

155 + a = 180 (angles on a straight line)

a = 180 - 155

a = 25 degrees

solving for the angles in the triangle

z + a + b = 180

60 + 25 + b = 180

b = 180 - 60 - 25

b = 95 degrees

b + ? = 180  (angles on a straight line)

? = 180 - 95

? = 85 degrees

Learn more on angles here:

https://brainly.com/question/27962469

#SPJ1

If a group of friends went to lunch at Burger Barn. The total bill was $57. If they want to leave a 22% tip, they will leave $14.25 for a tip.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.

Given that a group of friends went to lunch at Burger Barn. The total bill was $57. If they want to leave a 22% tip,

The tip price of the carton is,

tip price =  22%  of the bill

tip price =(25/100)× $57

tip price = $14.25

Thus, if a group of friends went to lunch at Burger Barn. The total bill was $57. If they want to leave a 22% tip, they will leave $14.25 for a tip.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

The answers obtained after correctly using the identities is given by,

if cosθ=0.9 and sinθ=0.7, then tan(−θ)= -7/9. If sinθ=1/4​, then -sin(−θ)= 1/4.

For the first question,
If cosθ=0.9 and sinθ=0.7, then tan(−θ)=?

We can use the identity tanθ = sinθ/cosθ.
Since tan(−θ) = -tanθ, we have tan(−θ) = -sinθ/cosθ.
Plug in the given values for sinθ and cosθ,
tan(−θ) = -0.7/0.9
Simplify the expression,
tan(−θ) = -7/9

For the second question,
If sinθ=1/4​, then -sin(−θ)=?

We can use the identity sin(-θ) = -sinθ.
Plug in the given value for sinθ,
-sin(−θ) = -(-1/4)
Simplify the expression,
-sin(−θ) = 1/4

So, if cosθ=0.9 and sinθ=0.7, then tan(−θ)= -7/9. If sinθ=1/4​, then -sin(−θ)= 1/4.

Learn more about "identities": https://brainly.com/question/7331447

#SPJ11

Answer:

y=1/2x-2

Step-by-step explanation:

2y=-4+x

2y=x-4 divide both sides by 2

y=1/2x-4/2

y=1/2x-2

Answer:

\(y = 0.5x - 2\)

Step-by-step explanation:

Slope intercept form is

\(y = mx + b\)

Our initial goal is to isolate y.

\(2y - x = -4\)

Add x to both sides of the equation.

\((2y - x) + x = (-4) + x\)

Simplify.

\(2y =x -4\)

Divide both sides by 2.

\(\frac{2y }{2} = \frac{(x - 4)}2}\)

Simplify.

\(y = 0.5x - 2\)

Green, Inc.'s qualifying research expenditures for the year can be calculated by adding the in-house research expenditures to the payments made to a qualified research organization, such as the Blue Foundation.

Using this formula, we can calculate the qualifying research expenditures for the year as follows:

$60,000 + $30,000 = $90,000

Therefore, the answer is (d) $90,000.

In-house research expenditures, such as wages, supplies, and computer time, qualify as research expenditures for tax purposes. Payments made to a qualified research organization also qualify as research expenditures. To determine the total qualifying research expenditures for the year, these two types of research expenditures must be added together.

In the given scenario, Green, Inc. incurred $60,000 in in-house research expenditures and paid $30,000 to the Blue Foundation for research. Adding these two amounts together, the qualifying research expenditures for the year are $90,000.

Learn more about expenditures here: brainly.com/question/32066267

#SPJ11