Which of the following are continuous functions of time?
The quantity of gas in the tank of a car on a journey between New York and Boston (continuous or discontinuous)
The number of students enrolled in a class during a semester (continuous or discontinuous)

I want to verify my answers:
Discontinuous for the car
Continuous for the students,

Answers

Answer 1

Continuous functions of time are a function if small changes are made to the source then the result will have those small changes in them. The quantity of gas is a continuous function of time because small variations can be made to the quantity of the gas in use to the extent of molecules and atoms whereas same cannot be done to the student as we cannot half them.

Answer 2

Final answer:

The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.

Explanation:

Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.

Related Questions

If GH = 3 and HJ = 5, then G ___ J.

Choose the relationship symbol that would make a true statement.

Answers

it will be less than

Step-by-step explanation:

The given equation is as follows.

GH = 3 and HJ = 5

Therefore, simplify for H from both the equations as follows.

H = [tex]\frac{3}{G}[/tex] .......... (1)

and, H = [tex]\frac{5}{J}[/tex] .......... (2)

Equating both equation s(1) and (2), we get the following.

[tex]\frac{3}{G}[/tex] = [tex]\frac{5}{J}[/tex]

G = [tex]\frac{3J}{5}[/tex]

or, G = 0.6J

This means that J will be 0.6 times greater than G.

Thus, we can conclude that G < J.

Compare the values of the underlined digits.

34,258 and 47,163
- -

The value of 4 in _________ is______ times the value of 4 in ________

PLEASE ANSWER ASAP IT'S FOR MY SISTER

Answers

In the first number, the "4" is in the thousands place - meaning it is 4,000 + 30,258
In the second number, the "4" is in the ten thousands place - meaning it's
40,000 + 7,163.
40,000/4,000 = 10
The value of 40,000 in the second value is 10x greater than the value of 4,000 in the first value.

I'll give you brainliest answer!! Help me. This diagram shows a smaller square inscribed within a larger square.
Answer with supporting work:

Answers

Each side of the smaller square is the hypotenuse of the triangles with legs of 3 and 4. From the Pythagorean Theorem, we can calculate the hypotenuse:
hypotenuse^2 = 3^2 + 4^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Therefore, the area of the smaller square is 5 * 5 = 25

The answer would be 256 as the area because roughly the 4 closes in onto the smaller square which makes it 4 x 4 so what I would do is go first 4 x4 which equals 16 and then do it over 4 x 4 equals 16 once again so 16 x 16 equals 256 your welcome!!!!! :)

There are seven black marbles and nine white marbles in a bag what is the aprroximate probability of drawing two black marbles and then a white marble without replacement

Answers

There are a total of 16 marbles in the bag. Black marbles compound 7/16 or 43.75% of the bag. White marbles compound 9/16 or 56.25% of the bag.

There is a probability of 43.75% to pick a black marble in the bag with 16 marbles.
If you do , there will be 6 black marbles and 9 white marbles left in the bag. The probability to pick anpther black marble is 6/15 or 40%.

If you do pick another black marble , there will be 5 black marbles and 9 white marbles left in the bag , which means the probability of you getting a white marble next is 9/14 or 64.28%.

Now we just have to multiply the probability of you picking the marbles in the right order :

0.4375 × 0.4 × 0.6428 = 0.11249

Which is approximately 11.25%

There is a probability of 11.25% of you getting two black marbles and one white marble in a bag with 7 black marbles and nine white marbles .

I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you :)

The approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.

What is probability?

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of black marbles = 7

Number of white marbles = 9

The event of drawing two black marbles from seven black marbles is

⇒ [tex]\frac{7C_{2} }{16C_{2} }[/tex]

[tex]7C_{2} =\frac{(7)(6)}{(1)(2)}[/tex]

⇒ 21

[tex]16C_{2}=\frac{(16)(15)}{(1)(2)}[/tex]

⇒ 120

Now, [tex]\frac{7C_{2} }{16C_{2} }=\frac{21}{120}[/tex]

Total number of balls, after drawing 2 black balls without replacement is

⇒ 16 - 2 = 14

The event of drawing a white marble without replacement from nine white marbles is

[tex]\frac{9C_{1} }{14C_{1} } = \frac{9}{14}[/tex]

Thus, the approximate probability of drawing two black marbles and then a white marble without replacement is

P(E) = [tex](\frac{21}{120}) (\frac{9}{14} )[/tex]

⇒ 9/80

Hence we can conclude that the approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.

Learn more about probability here

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You bought a coat at $78.50 and two shirts at $21.99 each. if the sales tax rate is 7%, how much is the total purchase?

Answers

7% of the coat is $5.49. 7% of the shirts is $1.54 each. adding up the taxes ($8.57) with the base total ($122.50) would add up to $131.07

Answer:

The answer is going to be $131.05

Step-by-step explanation:

I just took the test

Factor completely x2 - 8x + 16

A. (x+4)(x+4)
B. (x-4)(x-4)
C. (x+4)(x-4)
D. (x-2)(x-8)

Answers

B (x-4)(x-4)

When you take -4+-4, you will get -8 and when you multiply -4 x -4, you will get 16

What is the measure of ∠EGF?

What is the measure of ∠CGF?

Answers

measure of ∠EGF = 1/2( 180 - 50)
= 1/2(130)
= 65

the measure of ∠CGF = 180 - 65
= 115

Hello!

This is an isosceles triangle, which means its base angles are congruent. Interior angles of triangle add to equal 180 degrees, so you can make an equation to solve for the measure of the base angles. I'll call the base angles x.

180 = 50 + 2x
130 = 2x
65 = x

That gives you m∠EGF and m∠FGE (65°).

To find m∠CGF, you must know that it and ∠EGF are supplementary (they add to equal 180 degrees). Make another equation setting them to equal 180 using m∠EGF (65°):

180 = 65 + x
115 = x

Answer:
m∠EGF = 65°
m∠CGF = 115°

Rotate this image 90 clockwise around the point (-1 1 )

Answers

To rotate clockwise 90 degrees from a point (x, y) the image will be (y, -x)

In this case given the point (-1, 1), the image will be (1, -(-1)) or (1, 1)

Answer: You didn't put options A, B, C, OR D

no picture either

Step-by-step explanation:

Can someone please help me out on this?

Answers

(Y>x/3+0) - I think the answer B

I hope it can help you.

PLEASE HELP ASAAAAPPPPPP

Answers

the correct answer is A

the answer is A hope it helps

AC is tangent to circle O at A. If mBY =24, what is m

Answers

the correct question in the attached figure

we know that
the inscribed angle measures half of the arc it comprises.
then
m∠YAB=(1/2)*m∠BY-------------> m∠YAB=(1/2)*24°=12°
m∠YAC=90°-m∠YAB=90°-12°=78°

the answer is the option C) 78°

What is the correct definition of the third quartile of a data set?
A. The third quartile is all the numbers of the data set added together and divided by 3. B. The third quartile is the difference between the maximum and median. C. The third quartile is the median of the upper half of data in the data set. D. The third quartile is the mode of the upper half of data in the data set.

Answers

we know that

The third quartile (also called the upper quartile) has 75 percent of the data below it and the top 25 percent of the data above it. The third quartile is the same as the median of the part of the data which is greater than the median.

therefore

the answer is the option
C.) The third quartile is the median of the upper half of data in the data set.

Answer:

Option: C is the correct answer.

C. The third quartile is the median of the upper half of data in the data set.

Step-by-step explanation:

We know that our data is divided into three quartiles:

First quartile or lower quartile--

It is the median of the lower set of the data.

Middle quartile or Median--

Median is the central tendency of the data and it always exist in the middle of the data set.

Third quartile or upper quartile--

It is obtained by finding the median of the upper set of the data.

Hence, the answer is: Option: C

please help me thank you.

Answers

∠AOC is a "central angle".

_____
Any angle with sides that are radii and a vertex at the center of the circle is a central angle.

Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for what other family of functions?

Exponential
Linear
Rational
Polynomial

Answers

They are going to be very similar to rules governing exponential functions. This is due to the fact that logarithms in essence "cancel" exponents.

Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for the exponential family of function.

This comes from the definition of logarithm itself which says that a logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Let us illustrate this by way of an example. We know that 100 can be represented as [tex] 10^2 [/tex]. Here 10 is the base, 2 is the power and 100 is the given number. Therefore,

[tex] 10^2=100 [/tex]

Likewise, we can represent 1000 as [tex] 1000=10^3 [/tex]

Now, if we multiply [tex] 10^2 [/tex] and [tex] 10^3 [/tex] we will get: [tex] 10^2\times 10^3=10^{2+3}=10^5 [/tex]. We added the powers. Therefore, the logarithm of [tex] 10^5 [/tex] to the base 10 is 5.

Let us see if we will get the same result by using the rules of logarithms.

[tex] log(10^2\times 10^3)=log(10^2)+log(10^3)=2log(10)+3log(10)=2+3=5 [/tex]

As we can see we got the same result by using the logarithm and the exponential rule, thus, verifying our answer. Similar results can be obtained for other operations of the logarithmic rule.

Suppose the dial on the spinner is spun 2 times in a row.

X is the number of times the dial lands on region A.

Which table represents the probability distribution for the variable X?

Answers

If you spin the dial two times there three things that can happen:
1) Dial does not land in the region A
2) Dial lands once in the region A
3) Dial lands twice in the region A
The combined probability of these three events has to be 1.
Let's calculate probabilities of each event:
[tex]1) P=P(1,1)=\frac{2}{3}\cdot\frac{2}{3}=\frac{4}{9}\\ 2)P=P(1,2)+P(2,1)=2\cdot \frac{2}{3}\cdot \frac{1}{3}=\frac{4}{9}\\ 3)P=P(3,3)=\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{9}[/tex]
If we summ all those probabilities we get 1.
The answer would table C (lower left corner).

if this is your spinner the answer is

the answer is

X P

0 1/9

1 4/9

2 4/9

The mean of the data set is 18 what’s the missing number 21,11,blank,27,22,13,16

Answers

9514 1404 393

Answer:

Step-by-step explanation:

The sum of the 7 numbers needs to be 7·18 = 126.

Then the missing number is ...

126 -21 -11 -27 -22 -13 -16 = 16

The point nearest to the origin on a line is at (4, -4). Find the standard form of the equation of the line.

Answers

The line through that point and the origin has a slope of -1. It is perpendicular to the line you want, so the line you want has slope +1. Its equation can be written as
.. y = (x -4) -4
or, in standard form
.. x - y = 8

Find the inverse of the following function. f(x) 8√ x for x > 0

Answers

The inverse of the function f(x) = 8√x for x > 0 is g(x) = x^2/64.

To find the inverse of the function f(x) = 8√x for x > 0, we need to interchange the roles of x and y and solve for y.

Let's start by rewriting the function using y instead of f(x):

y = 8√x

Next, we'll swap x and y:

x = 8√y

To isolate y, we can square both sides:

[tex]x^2 = (8\sqrt y)^2\\\\x^2 = 64y[/tex]

Now, divide both sides by 64:

[tex]x^2/64 = y[/tex]

Simplifying further:

[tex]y = x^2/64[/tex]

Therefore, the inverse of the function f(x) = 8√x for x > 0 is given by [tex]g(x) = x^2/64.[/tex]

To know more about inverse, refer here:

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15. The following statements concerning the location of an extreme value of a twice-differentiable function, f, are all true. Which statement also includes the correct justification?

(A) The function has a maximum at x=5 because f'(5)=0.
(B) The function has a maximum at x=5 because f'(x)<0 for x<5 and f'(x)>0 for x>5.
(C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal.
(D) The function has a minimum at x=3 because f'(x)<0 for x<3 and f'(x)>0 for x>3.
(E) The function has a minimum at x=3 because f"(3)<0.,

Answers

(D) The function has a minimum at x=3 because f'(x)<0 for x<3 and f'(x)>0 for x>3. Let's look at the available options and see why the justification is either correct or incorrect. (A) The function has a maximum at x=5 because f'(5)=0. * We've been told that the first derivative f'(x) is zero at x=5. That means that there's a possibility of f(5) being either a local maximum or a local minimum. But that's not a guarantee of either happening since it's possible for the function to simply have a slope of 0 for a brief instant while the function either increases or decreases. In any case, the fact that the first derivative is 0 is a necessary, but not sufficient condition for a local maximum to occur at that point. So this is a bad choice. (B) The function has a maximum at x=5 because f'(x)<0 for x<5 and f'(x)>0 for x>5. * Let's look at the values. We've been told that f'(x) < 0 for x<5. That means that the value of the function is decreasing since the slope is negative. And for f'(x) > 0 for x > 5 means that the slope then increases. That would indicate that f(5) is a local minimum, not a local maximum. So this is also a bad choice. (C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal. * Having the slope being zero at a point means that one of 3 things is happening at that point. 1. The point is a local minimum, 2. The point is a local maximum. 3. The point is an inflection point. Since there's multiple possibilities, that means we can't know that the actual situation is one of the point being a local minimum without more information. So this too is a bad choice. (D) The function has a minimum at x=3 because f'(x)<0 for x<3 and f'(x)>0 for x>3. * Since the slope of f(x) is negative for x < 3, that means that the value is decreasing over that range. And then the slope becomes positive for x>3, so the value is increasing. Therefore the local minimum value happens at x=3, which agrees with the statement. So this is the correct choice. (E) The function has a minimum at x=3 because f"(3)<0., * OK, we've been given the sign of the second derivative. Since it's negative, that indicates that the value of the first derivative is decreasing. But it doesn't give us any information about the first derivative having a value of 0, so we don't know if there's anything special about f(3). So this is a bad choice.

Instructions:Select the correct answer from each drop-down menu. The sum of the squares of two consecutive positive even numbers is 340. Find the numbers. The consecutive even numbers are

Answers

Looking at the problem, you can come up with an equation for the consecutive numbers.

[tex] x^{2} + (x + 2)^{2} = 340[/tex]

If we expand the second term:
[tex] x^{2} + x^{2} + 4x + 4 = 340[/tex]

Combine like terms:

[tex]2 x^{2} + 4x + 4 = 340[/tex]

You can reduce this by dividing both sides of the equation by two:

[tex] x^{2} + 2x + 2 = 170[/tex]

And we transpose 170 to get a standard quadratic form that the right side will be zero:
[tex] x^{2} + 2x - 168 = 0[/tex]

Then factor the left side:
[tex](x +14)(x-12) = 0[/tex]

Find out the values of x that makes each factor = 0
x + 14 = 0
x = -14

We can eliminate the negative symbol because the problem is asking for positive even integers.

and;

x - 12 = 0
x = 12

Now we can say that the first positive integer is 12 and the second one is 14

lets name the numbers as x and x + 2
the sum of the squares of these 2 numbers are 340
x² + (x+2)² = 340
x² + x² + 4x + 4 = 340
2x² + 4x - 336 = 0
we are left with a quadratic equation
coefficient of x is 2 therefore divide each number by 2
x² + 2x - 168 = 0
to solve the quadratic equation , the 2 factors whose product is 168x² and sum is 2x is -12x and 14x
x² + 14x -12x -168 = 0
x (x + 14) - 12(x + 14)=0
(x+14)(x-12) = 0
we have 2 possible values for x
x + 14 = 0 x-12 = 0
x = -14 x = 12
from the 2 answers the correct answer is x = 12 as it should be a positive integer
one integer is 12 and consecutive even integer is 14
to check the product of the squared numbers
= 14² + 12²
= 196 + 144
= 340

The table below shows the data collected on the number of car washes, y, each day since the Auto Spa opened, x.

Days Since Auto Spa Opened 0 20 40 60 80 100
Number of Car Washes 29 35 18 31 28 14

The owner of the new Auto Spa created a line of best fit for the data that can be modeled by the following equation.

y = -0.12x + 31.76

Match the slope and y-intercept with the correct description for the given situation.

titles
the number of cars washes on the day the Auto Spa opened

the ratio of car washes to the number of days since the Auto Spa opened

the number of car washes

the total number of days since the Auto Spa opened

the ratio in the number of days since the Auto Spa opened to the total profit

pair
y-intercept

slope

Answers

The slope is the ratio of car washes to the number of days since Auto Spa opened; and the y-intercept is the number of car washes on the day the Auto Spa opened.

Explanation:
This line of best fit is in slope intercept form: y=mx+b, where m is the slope and b is the y-intercept.

In this equation, m corresponds with -0.12 and b corresponds with 31.76.

The slope is the ratio of change in y to change in x. The y-coordinate of each point represents the number of car washes and the x-coordinate represents the number of days since Auto Spa opened; the ratio of change in y to change in x is then the ratio of the number of car washes to the number of days since Auto Spa opened.

The y-intercept is the point where the data crosses the y-axis; at this point, and all on the y-axis, the x-coordinate is 0. In this problem, the x is the number of days since Auto Spa opened; if it is 0, this means 0 days since it opened, which would be its opening day. Thus the y-intercept is the number of car washes on opening day.

Answer:

The slope is the ratio of car washes to the number of days since Auto Spa opened; and the y-intercept is the number of car washes on the day the Auto Spa opened.

Step-by-step explanation:

The measure of a minor arc is equal to the measure of __________

Answers

The measure of a minor arc is less than 180º

Convert the fraction to decimal and decimal into the fraction 10.222

Answers

10.222=10 and 222/1000
I'm not sure if that's what you were looking for but I hope this helps!

Answer:

10 and 222/1000

Step-by-step explanation:

Your school drama club is putting on a play and hopes to raise $600 from ticket sales. They sell adult tickets for $8 each and student tickets for $5 each. Let x represent the number of adult tickets and y represent the number of student tickets. The equation to represent the number of tickets sold to reach their goal, 8x+ 5y = 600, is graphed below. If 40 adult tickets are sold, how many student tickets must be sold to reach their goal?

Diagram can be shown here:
https://static.k12.com/eli/bb/343/3_23939/2_15013_4_23943/d7066d09bfa7bf4e8df2b2c0b508a3e8ba21c76d/media/b1cd8381087979f1dffbcd6f3efef158a61fbd57/mediaasset_649354_1.gif

Answers

8x40=320 +280=600 5x50=250 +5x6=30 320+250+30+600 so they will have to sell 40 adult tickets and 256 student tickets to accomplish their goal

which reason justifies the last step in a proof that ΔEDG≌ΔADC?

Answers

it is side angle side postulate
fd is congruet to db
ed is congruent to da
and vertical angles theorem

Write the polynomial in standard form. Then name the polynomial based on it's degree and number of terms.

3 - 10x^2 - 7x + 3x^2

Answers

In standard form...
-7x^2 - 7x + 3

This is a trinomial because it has 3 terms.
The degree of this polynomial is 2.

What is the maximum number of real zeros that a function with degree 5?

Answers

5 for example
y = (x - 22)(x - 1)(x + 1)(x - 2)(x+2)

A lake has the capacity to support 10,000 trout. Suppose that the conditions are such that the current population of trout will grow logistically up until it stabilizes at the amount that the lake can support. Currently there are 1,500 trout in the lake. Which of the following is a possible model for P(t), the trout population in t years?

Answers

I just got this problem, I'm not sure if it's right but I got P(t) = 10,000/ (1+9e^0.48t)

Answer:

P(t) = 10,000/ (1+9e^-0.48t)

Step-by-step explanation:

i think because it starts at around 1500 for t=1 and then when t=2 and so on it grows exponentially.

For which data representation is the median the better measure of center

Answers

Answer: The second graph

In all but the 3 graphs, the data is perfectly symmetrical. This means that the mean and the median would be the same.

However, in the second graph the data is skewed to the right. This means that the mean would also be skewed to the right due to the larger scores there. Using the median in this case would give a clearer picture of the data.

(x 2 + 2x - 1)(x 2 + 2x + 5) Please help asap!

Answers

Hi there!

To solve this equation, we can use distributive property.

I listed the terms you have to multiply :
x² × x² = x^4
x² × 2x = 2x³
x² × 5 = 5x²
2x × x² = 2x³
2x × 2x = 4x²
2x × 5 = 10x
-1 × x² = -x²
-1 × 2x = -2x
-1 × 5 = -5

Add all of them....
x^4 + 2x³ + 5x² +2x³ + 4x² + 10x - x² - 2x - 5
add up the like terms to simplify

x^4 + 4x³ + 8x² + 8x - 5

Hope this helped! :)

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What is the length of CC' ? Odysseus uses his cleverness to advance the plot in all of the following events EXCEPTA.he lies about his name to the Cyclopes B.He enters the archery contest C.he ask Circes adviceD.he escapes the Sirens I think its C How many times can 3 go into 9 Please help ASAP!!! 36 points! (: Which of the following statements about the Japanese attack on Pearl Harbor is true?The attack on Pearl Harbor marked the first time an atomic bomb was used in a war.The United States was unprepared, and most of the U.S. fleet was destroyed.The United States expected the attack, but was still overwhelmed by Japanese troops.The Japanese had the backing of the German navy during the attacks. Jefferson Park sits on one square city block that measures 300ft on each side. Sidewalks join opposite corners. About how long is each diagonal sidewalk? What part does color usually play in preschool childrens artwork? what idea did W.E.B Du bois put forward as a way for african americans to improve their condition The number of frogs in a swamp ecosystem increased sharply. Soon, the frogs exceeded the carrying capacity of the ecosystem. How will this situation affect the ecosystem? What percent of 12.5 is 39 If 5 lemons are used to make a gallon of lemonade,how many lemons are needed to make 3 gallons Mrs. jones left her purse unattended and went into the other room. what is revealed by her action? A policeman's whistle has a _____. high pitch low amplitude low pitch Is the Hertzsprung-Russell diagram still a valid instrument in studying stars, given that it is over 100 years old? 10. Read the following passage from the Odyssey:Tell me, where was it, now, you left your ship around the point, or down the shore, I wonder? He thought hed find out, but I saw through this, and answered with ready lie: Poseidon Lord, who sets the earth a-tremble, broke it up on the rocks at your lands end. A wind from seaward served him, drove us there. We are survivors, these good men and I.From this passage, the reader is most likely to determine that (1 point)Odysseus is not easily fooled.the men will escape from the Cyclops cave.the Cyclops is not very intelligent.the Cyclops plans to keep the men as his prisoners. Which sentence has a subject-verb agreement error? A)A man in a strange cloak and hat is walking on our back porch tonight! B)One of my sister's friends that she made in her college sorority are a doctor. C)The politicians who had supported the disastrous policies apologized profusely. D)The villagers who were sick with dysentery were cared for by the local Jesuit priests. At the apple pan 4 burgers and 3 fries cost 26.50. 5 burgers and 5 fries cost $36.25. what is the cost for each item? Which was an idea used to promote the theory of plate tectonics Carl ran 27 miles last week. This is 3 times farther than Anna ran. Which equation can be used to find how many miles Anna ran? Which of the following BEST explains why punch-card voting is no longer legal?