A moving sidewalk in an airport moves people between gates. It takes Jason's 6-year-old daughter Josie 45 sec to travel 180 ft walking with the sidewalk. It takes her 11 sec to walk 22 ft against the moving sidewalk in the opposite direction). Find the speed of the sidewalk and find Josie's speed walking on non- moving ground

Answers

Answer 1

Speed of sidewalk = 1 ft/sec

Therefore, the speed of the moving sidewalk is 1 ft/sec, and Josie's speed walking on non-moving ground is 3 ft/sec.

To find the speed of the moving sidewalk, we can use the formula:

distance = rate x time

For Josie walking with the sidewalk, we know that she traveled 180 ft in 45 seconds, so:

180 = (speed of sidewalk + Josie's walking speed) x 45

Simplifying, we get:

4 = speed of sidewalk + Josie's walking speed

For Josie walking against the sidewalk, we know that she traveled 22 ft in 11 seconds, so:

22 = (Josie's walking speed - speed of sidewalk) x 11

Simplifying, we get:

2 = Josie's walking speed - speed of sidewalk

Now we can solve for both the speed of the sidewalk and Josie's walking speed. Adding the two equations we have:

4 + 2 = 2Josie's walking speed

6 = 2Josie's walking speed

Josie's walking speed = 3 ft/sec

Substituting this back into one of the equations, we can find the speed of the sidewalk:

4 = speed of sidewalk + 3

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Related Questions

what is 654,984 × 548,784,844 × 99,999 ?

Answers

Answer:

3.594417e+19

Step-by-step explanation:

Harry invests £6000 in a savings account. The account pays 3.4% compound interest per year. Work out the value of his investment after 3 years. Give your answer to nearest penny?

Harry invests 6000 in a savings account. The account pays 3.4% compound interest per year. Work out the

Answers

Answer is?

3.6 maybe?

3 Consider the line y= 3/4x+3. Find the equation of the line that is perpendicular to this line and passes through the point (-8, 6).

Answers

ANSWER

\(y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3}\)

EXPLANATION

We have to find the equation of the line perpendicular to the given line:

\(y\text{ = }\frac{3}{4}x\text{ + 3}\)

and passes through the point (-8, 6)

A line perpendicular to another line has a slope that is the negative inverse of the line.

The slope of the given line is 3/4, so the slope of the line we are looking for is -4/3

Now, we use the point slope method to find the equation:

y - y1 = m(x - x1)

where m = slope

(x1, y1) = point the line passes through

So, we have:

\(\begin{gathered} y\text{ - 6 = -}\frac{4}{3}(x\text{ - (-8))} \\ y\text{ - 6 = -}\frac{4}{3}(x\text{ + 8)} \\ y\text{ - 6 = -}\frac{4}{3}x\text{ + (-}\frac{4}{3}\cdot8) \\ y\text{ - 6 = -}\frac{4}{3}x\text{ - }\frac{32}{3} \\ \Rightarrow\text{ y = -}\frac{4}{3}x\text{ - }\frac{32}{3}\text{ + 6} \\ y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3} \end{gathered}\)

That is the equation of the line.

help me at this thanks​...please this is an urgency

help me at this thanks...please this is an urgency

Answers

Answer:

if simplified is 30

Step-by-step explanation:

600 x 360/7,200

^^^^
What he said....

How instructional context can impact learning with educational technology: Lessons from a study with a digital learning game.

Answers

The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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what is 7 1/2 as a decimal.. please!!

Answers

Answer:

Your answer is 7.5 as a decimal

Step-by-step explanation:

mark 4 brainly

Answer:

7.5

Step-by-step explanation:

Here you go here is the answer

lol another math problem i need help on

lol another math problem i need help on

Answers

Answer:

32x - 8

Step-by-step explanation:

8 x 4 = 32

(-)2 x 4 = -8

32x - 8

hope this helps and that it's right :)

what is the measure of lmn in kite klmn? 49° 99° 106° 155°

Answers

155^A.The measure of LMN in kite KLMN is 155°.

A kite's main characteristic is that it has two pairs of congruent adjacent sides, with one set of diagonally opposite angles being equal, but the other set not. In a kite, these angles have different degree measures.

Kite KLMN has two pairs of adjacent sides that are congruent, and its diagonal is not perpendicular. So, angle KLM is 106°, angle KLN is 99°, and angle KMN is 49°. Since the sum of the internal angles of a quadrilateral is 360 degrees, we can use the following formula to calculate the angle LMN:360 - (angle KLM + angle KLN + angle KMN) = angle LMN360 - (106° + 99° + 49°) = 106°.Therefore, the measure of LMN in kite KLMN is 155°.

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sented in the following table by the sex of the child. boys girls make good grades 192 590 be popular 64 90 be good in sports 188 80 the expected count for boys who make good grades is group of answer choices 388.38 444 288.38 56.79

Answers

The expected number of boys who make good score is found to be 188 by using random sample method.

To get the projected number of boys who get good grades, multiply the total number of boys by the proportion of boys who answered they would like to get good grades the most.

According to the table, the total number of boys surveyed is:

188 +64 +192 = 444

And the percentage of guys who indicated they

would like to get good grades is:

188/444 0.423

As a result, the projected number of guys with good grades is:

Expected number of boys = total number of boys

x percentage of boys who get high grades

444 x 0.423 = 444 boys expected

Number of boys expected = 187.812

When we round to the nearest full number, we get: The expected number of males with good grades

is 188.

So, as a result there are 188 boys who say they

would like to score more good grades.

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Complete question - A study examines the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achievement of personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented in the following table by the sex of the child.

Boys Girls

Be good in sports 188 590

Be popular 64 80

Make good grades 192 90

Problem 4.2
A textbook has 428 numbered pages, starting with 1.



A textbook has 428 numbered pages, starting with 1.

You are equally likely to stop on any of the pages if you flip through the book randomly.
What is the probability that you turn to an even-numbered page?

Answers

Answer:

50%

half of the numbers are even

Step-by-step explanation:

Find an equation of the tangent line to the curve at the given point. y = x^3 ? 3x + 2, (4, 54) Please show work

Answers

The slope of the tangent line at (4, 54) is 45. So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to use calculus. First, we find the derivative of the function:

y' = 3x^2 - 3

Next, we plug in x = 4 to find the slope of the tangent line at that point:

y'(4) = 3(4)^2 - 3 = 45

So the slope of the tangent line at (4, 54) is 45. To find the equation of the line, we use the point-slope form of the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in our values, we get:

y - 54 = 45(x - 4)

Simplifying, we get:

y - 54 = 45x - 180

y = 45x - 126

So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to first find the derivative of the function and then use the point-slope form of a line.

1. Find the derivative of the function with respect to x:
y'(x) = d/dx (x^3 - 3x + 2) = 3x^2 - 3

2. Evaluate the derivative at the given point (4, 54) to find the slope of the tangent line:
m = y'(4) = 3(4)^2 - 3 = 3(16) - 3 = 48

3. Use the point-slope form of a line (y - y1 = m(x - x1)):
y - 54 = 48(x - 4)

4. Simplify the equation:
y - 54 = 48x - 192
y = 48x - 138

So, the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 48x - 138.

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Suppose you draw one card, put it back (and re-shuffle), and then draw another. What is the probability that the cards are of different suits

Answers

The probability that the two cards drawn are of different suits is approximately 0.3744 or 37.44%.

The probability that the first card drawn is of a particular suit (say hearts) is 13/52, because there are 13 hearts in the deck. The probability that the second card drawn is of a different suit (say diamonds) is 39/52, because there are 13 cards in each of the three remaining suits.

So, the probability that the first card is a heart and the second card is a diamond is (13/52) × (39/52) = 507/2704.

Similarly, the probability that the first card is a diamond and the second card is a heart is also (13/52) × (39/52) = 507/2704.

The probability that the two cards are of different suits is the sum of these two probabilities:

(507/2704) + (507/2704) = 1014/2704 ≈ 0.3744

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Question

Assuming you are drawing from a standard deck of 52 cards with 13 cards in each of the 4 suits (hearts, diamonds, clubs, and spades), the probability that the two cards drawn are of different suits can be calculated as follows:

Write the equation for a parabola with a focus at (-4,3)(−4,3)left parenthesis, minus, 4, comma, 3, right parenthesis and a directrix at y=5y=5y, equals, 5.

Answers

An equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

Given that, focus of a parabola at (-4,3) and a directrix at y = 5.

What is an equation of a parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where

The vertex of the parabola is (h, k)

The focus is (h, k + p)

The directrix is at y = k - p  

Here, the focus of the parabola is (4, -3)

The focus is (h, k + p)

So, h = 4

Then, k + p = -3 --------(1)

It has a directrix of y = 5

The directrix of the parabola is y = k - p

∴ k - p = 5 --------(2)

Add equations (1) and (2) to find k and p, that is

(k + k) + (p - p) = (-3 + 5)

⇒ 2k + 0 = 2

⇒ 2k = 2

Divide both sides by 2

k = 1

Substitute the value of k in equation (1), we get

1 + p = -3

Subtract 1 from both sides, we get

1 - 1 + p = -3 - 1

⇒ p = -4

Substitute the values of h=4, k=1 and p=-4 in (x - h)² = 4p(y - k), that is

(x - 4)² = 4(-4)(y - 1)

⇒ (x - 4)² = -16(y - 1)

Therefore, an equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

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Help me❤️!!!!!!!!!!!

Help me!!!!!!!!!!!

Answers

Answer:

B

Step-by-step explanation: Because for inverse functions, domain and range of functions exchange. In simple words, domain of function h(x) = range of inverse function & range of function h(x) = domain of inverse function.

Xander was in the lead for 75% of the laps during PE. If the race lasted 12 laps, how many laps did Xander lead?

Answers

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

Vance bought 2 packages of large beads and 1 package of medium beads. He bought 2 packages of large buttons and how many more beads than more buttons did vance buy

Answers

There are 472 more buttons bought by Vance than beads.

Define the term difference of number?One of the most crucial arithmetic operations, that is obtained by removing two integers, produces difference in mathematics.

For the stated question table is made.

So,

Total number of beads bought by Vance = Number of beads(2 packages of large beads) + Number of beads(1 package of medium beads).

= (2 × 96) + (1 × 64)

= 2 × (90 + 6) + 64

= (2 × 90) + (2 × 6) + 64

= 180 + 12 + 64

= 256 beads

Now,

Total number of buttons bought by Vance = Total number of buttons (2 packages of large buttons) + Number of buttons (2 packages of medium buttons)

= (2 × 56) + (2 × 38)

= 2 × (50 + 6) + 2 × (30 + 8)

= (2 × 50) + (2 × 6) + (2 × 30) + (2 × 8)

= 100 + 12 + 600 + 16

= 728 buttons

Thus,

Difference for the number of buttons and beads

= 728 – 256

= 472 beads

So,

Therefore, there are 472 more buttons bought by Vance than beads.

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Vance bought 2 packages of large beads and 1 package of medium beads. He bought 2 packages of large buttons

215 is what percent of 250?

Answers

The answer is 86% I hope you do well

215 is 86% of the number 250.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

To find the percentage that 215 represents out of 250, we can use the following formula:

percentage = (part/whole) x 100%

In this case, the "part" is 215 and the "whole" is 250.

Plugging those values into the formula, we get:

percentage = (215/250) x 100%

percentage = 0.86 x 100%

percentage = 86%

Hence, 215 is 86% of the number 250.

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What is the product of 2x 7/10

Answers

Answer:

x = 17/2 or 8.5

Step-by-step explanation:

Here is your problem:

2x = 10 + 7

First we are going to add 7 to both sides.

2x = 10 + 7

+7         +7

Second, we are going to simplify.

2x = 17 (because 10+7 is 17)

Lastly, we are going to divide both sides by 2.

2x = 17

/2     /2

Your answer will be:

x = 17/2 OR 8.5

I am between 2 and 10. I am a mixed number. I am closer to 8 than 4 if you take my fraction part away. I am an odd number what am i​

Answers

I am 6 1/9 Hope this helps

14+x = -9

X equals what?

Answers

Answer:

x=−23

Step-by-step explanation:

14+x=−9

Step 1: Simplify both sides of the equation.

x+14=−9

Step 2: Subtract 14 from both sides.

x+14−14=−9−14

x=−23

Answer:

-23

Step-by-step explanation:

14+x =-9

-14      -14

x = -23

The first 4 questions I solved them I just don’t know how to match them please match them for me

The first 4 questions I solved them I just dont know how to match them please match them for me

Answers

1b 2d 3a 4c

1) 2x+3=9

The first step is to subtract 3 from each side,

2x =6

x=3

So

1) b

2) 3x -3 =15 The next step is to add 3 to isolate 3x

3x =18

x=6

2) d

3) -2p +9=-11 Subtract 9 from both sides so that we isolate the -2p

-2p=-11-9

-2p=-20

2p=20

p=10

3) a

4) 11=-4m -9 Add 9 from each side..

11 +9=-4m

20=-4m

-20=4m

m=-5

4)c

An Assembly Line Has 10 Stations With Times Of 1, 2, 3, 4, …, 10, Respectively. What Is The Bottleneck Time? Please Show All Work!!!!
An assembly line has 10 stations with times of 1, 2, 3, 4, …, 10, respectively. What is the bottleneck time?
Please show all work!!!!

Answers

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

What is the bottleneck?

In economics terms, the bottleneck is a chain of supply of resources that wants the most extended time in the supply chain operation for specific demand. It also evaluated to estimate the supply chain throughput.

Through put time = Sum of all times=1+2+3+4+5+6+7+8+9+10=55

Given,

Assembly line has 10 stations

Throughput time is 55

The formula for bottleneck time is:

Bottle neck time = Total stations/Throughput time ×100

= 10/55 ×100

= 18.18%

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

An assembly line has 10 stations with times of 1, 2, 3, 4,...,10, respectively. What is the bottleneck time?

a. 18.18% of the throughput time

b. 100% of the throughput time

c. 550% of the throughput time

d. 50% of the throughput time

e. 1.82% of the throughput time

Use implicit differentiation to determine the value of dy/dx at point (3, 2) given function x xy = 2y

Answers

The value of dy/dx is equivalent to 3

Implicit differentiation

Functions are written in terms of dependent and independent variables. Given the following function below;

x + xy = 2y

Differentiate the function implicitly

1+(x dy/dx+y) = 2dy/dx

Expand

1+x dy/dx + y - 2dy/dx = 0

(x-2)dy/dx = -1-y

dy/dx = (1+y)/(x-2)

The value of the function at the coordinate point (3, 2) is expressed as;

dy/dx = (1+2)/(3-2)

dy/dx = 3/1

Hence the value of dy/dx is equivalent to 3

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Match the slopes and lengths of the side of polygon A’B’C’D’ to their values

Match the slopes and lengths of the side of polygon ABCD to their values

Answers

In the given polygon we have: Slope of A'B' = 5, Length of A'D' = 8.4, Length of C'D' = 5.4, Slope of B'C' = 0.25.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Enlargement is the term used when a dilatation results in a larger image.

Reduction occurs when a dilatation results in a smaller picture.

When the polygon ABCD is dilate by 1.2 units the slope of the segments of the polygon remains the same, whereas the length of the segments are multiplied by 1.2 units.

Thus.

Slope of A'B' = 5

Length of A'D' = 8.4

Length of C'D' = 5.4

Slope of B'C' = 0.25

Hence, in the given polygon we have: Slope of A'B' = 5, Length of A'D' = 8.4, Length of C'D' = 5.4, Slope of B'C' = 0.25.

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a truck traveled the first 120 miles of a trip at one speed and the last 220 miles at an average speed of 5 miles per hour less. the entire trip took 6 hours. what was the average speed for the first part of the trip?

Answers

The average speed for the first part of the trip is 60 miles.

Given:

1st leg DATA:

distance = 120 miles ;

rate = x mph ;

time = d/r = 120/x hrs

2nd leg DATA:

distance = 220 miles ;

rate = x-5 mph ;

time = 220/(x-5) hrs

hence the equation we frame is:

Equation:

120/x + 220/(x-5) = 6

120(x-5) + 220x = 6x(x-5)

120x - 600 + 220x = 6x² - 30x

-6x² + 340x + 30x - 600 =0

-6x² + 370x - 600 = 0

-3x² - 185x + 300 = 0

(3x-5)(x-60)

3x = 5 or x-60=0

x = 5/3 or x = 60

hence x-5 = 60-5

= 55 miles per hour.

Hence we get the answer as 60 miles.

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i need help with this question

i need help with this question

Answers

The average rate of driving from Newyork to Boston is d. 54 mph.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The distance you drive is proportional to the time.

We know, The arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Therefore,

The average rate of driving is,

= (216/4) mph.

= 54 mph.

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A summary of two stocks is shown.


Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metroplis, Ltd MTP 17.95 18.28 18.25
Suburbia, Inc SBR 5.63 5.88 4.98


Suppose you purchase 30 shares of Metropolis stock and 55 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks?
Day 2 is the best by $26.75.
Day 3 is the best by $26.75.
Day 2 is the best by $23.65.
Day 3 is the best by $23.65.

Answers

The solution is,  the unique price of the proportion is $10.37 even as within the promotion it is promoting at $18.25 consequently, The inventory is over-valued.

We have,

The following market and stock-specific statistics  10.37201

anticipated Return on company Y = Rf + Beta(Rm-Rf)

= zero.029+ 1.forty one*(zero.082)

= zero.14462

charge of the stock =Dividend/predicted to go back

= 1. 5/0.14462

= 10.37201

So the unique price of the proportion is $10.37 even as within the promotion it is promoting at $18.25 consequently, The inventory is over-valued.

A market is described as the sum overall of all the consumers and dealers in the region or place under attention. The vicinity may be the earth, nations, regions, states, or towns. The fee, fee, and fee of items traded are according to forces of delivery and demand in a marketplace.

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complete question:

use the following market and stock specific information to answer this question. assume you create your own portfolio made up of the four individual stocks shown below. the weighting of the porfolio is 30% stock w, 20% stock x, 20% stock y and 30% stock z. if a treasury bill currently sells for $970.05 and if firm y is expected to pay a constant annual dividend of $1.50 per share, and if the stock is currently selling for $18.25 per share, what is your opinion of the stock price?

Which graph shows the solution to the system of linear inequalities?

y < 2x – 5

y > –3x + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.

Answers

The graph of the system of inequalities can be seen in the image at the end.

How to get the graph of the system of inequalities?

Here we have the following system of inequalities:

y < 2x - 5

y > -3x + 1

So first we need to graph the two lines:

y = 2x - 5

y = -3x + 1

With dashed lines (because the symbols < and > are used).

And then we shade all the region below the line:

y = 2x - 5

And we shade the region above the line:

y = -3x + 1

So we will get the graph below:

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Which graph shows the solution to the system of linear inequalities?y &lt; 2x 5y &gt; 3x + 1On a coordinate

PLZZ HURRY NO LINKS !! Jocelyn created this spinner where there is an equal chance of landing on red, blue, yellow, and purple.



She decided to test her spinner to see if it was truly a fair spinner, and she recorded her results.

Number of Spins
Number of Times Landed on Purple
Number of Times Landed on Yellow
Number of Times Landed on Blue
Number of Times Landed on Red
100
18
22
24
36
200
44
54
47
55
500
127
133
119
121
1000
270
246
246
238


Which statement is BEST supported by Jocelyn's data?

A
The probability of the spinner landing on a certain color changes every time the spinner is spun because probability can change based on the previous spin.
B
The red section is the most likely to be landed on when the spinner is spun because it was landed on the greatest number of times out of 100 spins.
C
The probability of landing on any color of the spinner is 14
, but the relative frequency of each color does not show that because probability is a prediction that can have varied results.
D
After the spinner is spun 1000 times, the purple section has a probability of 27100
of being landed based on the the data, so purple is the section with the greatest likelihood of being spun.

PLZZ HURRY NO LINKS !! Jocelyn created this spinner where there is an equal chance of landing on red,

Answers

Answer:

The answer is C

Step-by-step explanation:

Based on the spinner used by Jocelyn, we can infer that C. The probability of landing on any color of the spinner is 14, but the relative frequency of each color does not show that because probability is a prediction that can have varied results.

What does the spinner show?

As a result of the number of times that each color was landed on by the spinner, we know that the probability of landing on any color is 14.

We cannot however show the relative frequency of each color being landed on because such a prediction would have varied results as probability is not a certainty.

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Which one of the following option is true and YY is equal to 3 x 5 has?

Answers

The given equation y = 3x + 5 has infinitely many solutions.

What is a linear equation in two variables?

If an equation is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Given: Linear equation y = 3x + 5

We know that,

The linear equation in two variables in the form of ax + by + c = 0

For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.

For x = 1, y = 3 × 1 + 5 = 8. Therefore, (1, 8) is another solution.

For y = 0, 3x + 5 = 0, x = -5/3. Therefore, (-5/3, 0) is another solution.

Clearly, for different values of x, we get various values for y. Thus, any value substituted for x in the given equation will constitute another solution for the given equation. So, there is no end to the number of different solutions obtained by substituting real values for x in the given linear equation. Therefore, a linear equation in two variables has infinitely many solutions.

Hence, the given equation y = 3x + 5 has infinitely many solutions.

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