The distance traveled varies directly with the time spent in motion when speed is held constant.
If d represents the distance traveled and t represents time, which equation would represent this variation?
If you travel 150 miles in 4 hours, what is the constant of variation?
If you continue traveling at a constant speed, how long will it take to travel 200 miles? Round to the nearest tenth of
an hour.
about hours
Intro
Done

Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

Answer is C

(-2,3)

Step-by-step explanation:

Answer:

(-8, 18)

Step-by-step explanation:

To solve this system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the two equations.

One way to do this is to multiply the second equation by a constant that will make the coefficient of x the same as in the first equation. In this case, we can multiply the second equation by -5, which will give us:

-15x - 10y = -60

Now we can add this equation to the first equation:

5x + 2y = -4

-15x - 10y = -60

-10x - 8y = -64

Dividing both sides by -2, we get:

5x + 4y = 32

Now we have one equation with only x and y, so we can solve for either variable.

Let's solve for y by subtracting 5x from both sides:

5x + 4y = 32

-5x = -5x

4y = 32 - 5x

Dividing both sides by 4, we get:

y = (32 - 5x) / 4

Now we can substitute this expression for y into one of the original equations to solve for x. Let's use the first equation:

5x + 2y = -4

5x + 2[(32 - 5x) / 4] = -4

Multiplying both sides by 4, we get:

20x + 2(32 - 5x) = -16

Simplifying, we get:

20x + 64 - 10x = -16

10x = -80

x = -8

Now we can substitute this value of x into either of the equations to solve for y. Let's use the first equation again:

5x + 2y = -4

5(-8) + 2y = -4

-40 + 2y = -4

2y = 36

y = 18

Therefore, the solution to the system of equations is (x, y) = (-8, 18).

Answer:

A =33 units^2

Step-by-step explanation:

The area of a rectangle is found by

A = l*w  where l is the length and w is the width

A = 5.5* 6

A =33 units^2

Answer:17.6 years

Step-by-step explanation:

i did it

Answer:

They aren't

Step-by-step explanation:

9/25 / 3= 3/8.3

3/10 x 3 = 9/30

none of those equal to each other

The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

We can use the method of finite differences to find a possible recursive formula for this sequence.

First, let's compute the first few differences:

f(4) - f(1) = 6

f(7) - f(4) = 6

Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:

f(1) = a(1)^2 + b(1) + c = 6

f(4) = a(4)^2 + b(4) + c = 12

f(7) = a(7)^2 + b(7) + c = 18

Solving for a, b, and c, we get:

a = 1

b = 5

c = 0

Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

learn more about recursive formula: https://brainly.com/question/29224065

#SPJ1

The probability of getting heads on any individual coin toss is always 1/2, So, given that Thor flipped heads on his first coin toss, the probability of him flipping heads on his second coin toss is still 1/2.

In probability theory, the concept you're referring to is known as the "Gambler's Fallacy" or the "Law of Averages." The Gambler's Fallacy is the mistaken belief that if an event has occurred more frequently in the past, it becomes less likely to occur in the future, or vice versa.

However, it's important to understand that the outcome of a fair coin toss is independent of previous tosses. Each coin toss has a fixed probability of landing on heads or tails, and the previous outcomes do not impact the future outcomes.

For example, if you flip a fair coin and get heads five times in a row, the probability of getting heads on the next toss is still 1/2. The coin doesn't "remember" its past outcomes, and each toss is a separate, independent event.

This principle applies to any fair coin, including the hypothetical scenario with Thor. Given that Thor flipped heads on his first coin toss, the probability of getting heads on his second coin toss remains 1/2. The outcome of the first toss has no influence on the second toss, as they are independent events with equal probabilities.

To learn more about probability

https://brainly.com/question/13604758

#SPJ11

Answer:

27/238 = n/100

Step-by-step explanation:

The standard deviation formula is derived from the variance formula, which is calculated by finding the sum of the squared deviations of each data point from the mean.

The standard deviation is simply the square root of the variance. This is because the variance is expressed in squared units, and the standard deviation is expressed in the original units of the data.

The equation used in the derivation of standard deviation is the formula for variance, which is given by:

Variance = ∑(x - μ)² / n

Where x is the individual data point, μ is the mean of the data set, and n is the number of data points in the set.

The standard deviation formula is simply the square root of the variance formula. The standard deviation formula is given by:

Standard deviation = √(Variance)

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Answer:

5 inches of wire.

Step-by-step explanation:

60/12 = 5

So at .05 an inch,  you can afford 5 inches at 25 cents

Please mark brainliest!

Answer:

b= -3

b=3/2=1.500

Step-by-step explanation:

step 1 . b • (2b + 3) -  9  = 0

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   3 .

     -18    +    1    =    -17  

     -9    +    2    =    -7  

     -6    +    3    =    -3  

     -3    +    6    =    3

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  6  

                    2b2 - 3b + 6b - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   b • (2b-3)

             Add up the last 2 terms, pulling out common factors :

                   3 • (2b-3)

Step-5 : Add up the four terms of step 4 :

                   (b+3)  •  (2b-3)

Answer:

A) exactly one solution-(-1/6,0)

Step-by-step explanation:

6x-y=-1

6x+y=-1

First, use elimination and cancel out the y-values:

you would get: 12x=-2

Divide both sides by 12: (12x/12)=(-2/12)--x=-1/6

x=-1/6

Now, subtitute the x-value into tje first equation to find the y-value:

6(-1/6)-y=-1

-1-y=-1

-1+1-y=-1+1

-y=0

-y/-1=0/-1

y=0

y=0

Answer:

-a^3-2a^2+6a-41

Step-by-step explanation:

Answer:

x = 7 ft

Step-by-step explanation:

\(tan 55=\frac{10}{x}\\x=\frac{10}{tan 55}\\x=7.0020\\x=7\)

Answer:

x=7

Step-by-step explanation:

3x-5/4=x+1/2

3x-5=2(x+1)

3x-5=2x+2

3x=2x+2+5

3x=2x+7

3x-2x=7

x=7

Step-by-step explanation:

\(\frac{3x - 5}{4} = \frac{x + 1}{2} \\ 2(3x - 5) = 4(x + 1) \\ 6x - 10 = 4x + 4 \\ 6x - 4x = 4 + 10 \\ 2x = 14 \\ \: \: \: x = \frac{14}{2} \\ x = 7\)

The probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of students in classroom 101 = 13+7 = 20

Total number of students in classroom 103 = 8+12 = 20

The probability of choosing a boy from both classrooms:

= 19/20

Choosing a girl from Classroom 101 and a boy from Classroom 103:

Since both are independent event.

Probability of choosing a girl from Classroom 101 = 13/20

Probability of choosing a boy from Classroom 103 = 12/20

The probability of choosing a girl from Classroom 101 and a boy from Classroom 103:

= (13/20)(12/20)

= 156/400

= 39/100

Similarly, the probability of Choosing a boy from Classroom 101 and a girl from Classroom 103:

= (7/20)(8/20)

= 56/400

= 7/50

Similarly, we can find remaining probability.

Thus, the probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

MN+NO=MO

Where N is the midpoint of MO

Therefore:

MN = NO

MN = 8

NO = 8

8 + 8 = MO

MO = 16

Now:

MO + OQ = MQ

If O is the midpoint of MQ:

MO = OQ

OQ = 16

Therefore:

MQ = 16 + 16 = 32

a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

To learn more about  area Click Here:  brainly.com/question/22469440

#SPJ11

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

More on volume of stacked books can be found here: https://brainly.com/question/1058070

#SPJ1

(a) Sketch the region of integration D: The graph of the region of integration D is given below. Please refer to the graph below for the bounded region D. 73

(b) Evaluate the double integral dad y: Given curves are: y = x, x = 3 and y = 7 − x².(i) The bounded region is shown below. Please refer to the graph below for the bounded region D.

(ii) To evaluate the double integral dady, we need to convert the given curves into the form x = f(y) and x = g(y).y = x and x = 3.

Thus, we have x = y and x = 3 respectively.

Now, we can rewrite the double integral dxdy as follows:dxdy = dydxWe are given that y = 7 − x². When x = y, we have y = 7 − y². Solving for y, we get y = (7 ± √33)/2.

Out of these two values of y, we take y = (7 − √33)/2 because this value is less than 3 (which is the upper bound of x).

So, the double integral da dy is given by:∫(a)₍(7-√33)/2₎³ ∫y³ dy dx = ∫(a)₍(7-√33)/2₎³ (x³)dx= (1/4)[(3 - √33)⁴ - (a³ - √33/3)⁴]

Therefore, the double integral da dy = (1/4)[(3 - √33)⁴ - (7 - √33)⁴].

Note: We used the fact that the limits of integration for the outer integral are 7 - x² and x. The limits of integration for the inner integral are y = x and y = (7 - x²).

Therefore, the limits of integration for the outer integral are a and 3 (which are the given bounds for x).

To know more about Integration  visit :

https://brainly.com/question/31744185

#SPJ11

The graph of the data set is in the image at the end, and it can be modeled by the quadratic:

y = 2*(x + 1)² - 3

Here we have the table:

x            y

-2,         -1

-1,          -3

0,           -1

1,             2

2,            7

The graph of it can be seen in the image at the end, there we can see that this seems to be a quadratic function

At the graph we also can see that (-1, -3) is te vertex, then if the leading coefficient is a, we can write the quadratic equation as:

y = a*(x + 1)² - 3

And we know that the equation passes throug (0, -1), replacing that we will get.

-1 = a*(0 + 1)² - 3

-1 = a - 3

-1 + 3 = a

2 = a

The function is:

y = 2*(x + 1)² - 3

Learn more about quadratic functions at:

https://brainly.com/question/1214333

#SPJ1

The two points at which the line intersects the curve are (2, -2) and (4/3, -4).

To find the coordinates of the point at which the line with a gradient of 3 intersects the curve y = 3x² - 7x after passing through the point (2, -2), we can set the equation of the line equal to the equation of the curve and solve for x and y.

The equation of the line passing through (2, -2) with a gradient of 3 can be written as:

y = 3x - 8

Substituting this equation into the curve equation, we get:

3x - 8 = 3x² - 7x

Simplifying the equation:

3x² - 10x + 8 = 0

We can solve this quadratic equation to find the values of x. Using factoring or the quadratic formula, we find:

(x - 2)(3x - 4) = 0.

Setting each factor equal to zero:

x - 2 = 0 --> x = 2

3x - 4 = 0 --> x = 4/3

So, there are two possible x-values where the line can intersect the curve: x = 2 and x = 4/3.

Now, we can substitute these x-values back into the equation of the line to find the corresponding y-values:

For x = 2:

y = 3(2) - 8 = 6 - 8 = -2

For x = 4/3:

y = 3(4/3) - 8 = 4 - 8 = -4

For similar question on intersects.

https://brainly.com/question/28744045

#SPJ11

Answer: 12 outcomes

Step-by-step explanation:

When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.

Answer:

yo did anyone have the answer

Step-by-step explanation:

Answer:

(B). between 2.5 and 3.0 and between 4.0 and 4.5.

Step-by-step explanation:

According to the Question,

From the given table it is clear that the value of function are

 x   |  f(x)  |   Sign

2.0 |  2.8  | Positive  

2.5 |  1.1    | Positive

3.0 | –0.8 | Negative

3.5 | –1.2  | Negative

4.0 | –0.3 | Negative

4.5 |  0.7  | Positive

Therefore, the correct option is B.

Answer:

(1,5)

Step-by-step explanation:

2x-3(x+4)=-13        y=1+4

2x-3x-12=-13          y=5

-x-12=-13

+12

-x=-1/-1

x=1

The probability that a randomly chosen contestant has a brown beard and is only in the beard competition is 0.402. The correct answer is option (D) 0.402.

Let B denote the event that a contestant has a brown beard, and M denote the event that a contestant is only in the beard competition. We are given:

P(B) = 0.406

P(M) = 0.509

P(B U M) = 0.513

We want to find P(B ∩ M), the probability that a contestant has a brown beard and is only in the beard competition. We can use the formula:

P(B U M) = P(B) + P(M) - P(B ∩ M)

Rearranging and substituting the given values, we get:

P(B ∩ M) = P(B) + P(M) - P(B U M)

= 0.406 + 0.509 - 0.513

= 0.402

Therefore, the probability that a randomly chosen contestant has a brown beard and is only in the beard competition is 0.402.

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1

See full text below

POSSIBLE POINTS: 1

Trevor was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Trevor also noted the contestants were signed up for the mustache competition later in the day.

The probability that a contestant has a brown beard is 0.406, the probability that a contestant is only in the beard competition is 0.509, and the probability that a contestant has a brown beard or is only in the beard competition is 0.513.

What is the probability that a randomly chosen contestant has a brown beard and is only in the beard competition?

0.915

0.582

0.004

0.402

O 0.103

O 0.441

Answer:113

Step-by-step explanation:

67-180=113