Keenan places 3 green marbles, 4 yellow marbles and 1 blue marble in a bag.
Keenan then adds 1 green marble and 1 yellow marble to the bag.
Does the probability that Keenan will randomly choose a yellow marble increase, decrease or stay the
same?
Circle one:
Increases
Decreases
Stays the same
Justify your answer.

Answer:

a) J':(-7,7) K':(-5,2) L':(-2,3)

b) The x coordinates remained the same, the y coordinates swapped from negative to positive.

Step-by-step explanation:

Aside: I'm using J', K', and L' to denote the new locations of J,K,L after the reflection.

When an object is reflected over the x-axis, it means it's positive points will flip to negative y space, and negative points will flip to positive y space.

That said, J, for instance, will have the same X-coordinate, but its Y-coordinate will flip from negative to positive. Doing this with every vertex mirrors the triangle over the X-axis.

Therefore, J:(-7,-7) will become J':(-7,7), and likewise with K and L becoming K':(-5,2) and L':(-2,3).

Answer:

Step-by-step explanation:

Explanation:

Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)

r = radius

h = height of cone

In this case,

r = 8 is the radius

h = 41

So,

SA = surface area

SA = pi*r^2 + pi*r*sqrt(r^2+h^2)

SA = pi*8^2 + pi*8*sqrt(8^2+41^2)

SA = 1250.936884057 use a calculator for this step

SA = 1251 square meters approximately

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

Answer:

Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.

Step-by-step explanation:

Answer: Tom is 46 years old and Jerry is 34 years old.

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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The statement that linear pairs of angles are always adjacent is true.

What are Linear Pairs?

The pair of angles formed when two lines intersect each other at a point,  are called Linear Pairs, the angles formed are adjacent to each other and they share a common arm.

It is asked in the question that linear pairs of angles are always adjacent and the answer is yes, it is a true statement as they have a common arm and an uncommon arm, the sum of the angles is equal to 180 degrees.

Hence, the statement that linear pairs of angles are always adjacent is true.

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Answer:

4^5 = 1024

Step-by-step explanation:

Answer:

3 \(\frac{2}{3}\) inches long

Step-by-step explanation:

Find how long the paper will be by dividing 11 by 3. This will find how much 1/3 of the 11 inch paper is.

11/3

= 3 \(\frac{2}{3}\)

So, if she cuts the paper, the paper will be 3 \(\frac{2}{3}\) inches long

Answer: a, c, and d

Step-by-step explanation: hard to explain

hope this helped :)

Answer:

The minimum data entry is, 26.

The maximum data entry is, 83.

Step-by-step explanation:

The stem-and-leaf plot provided is:

2 | 6

3 | 2

4 | 1 2 2 5 6 6 8

5 | 0 1 1 2 3 3 3 4 4 4 4 5 6 6 8 9

6 | 8 8 8

7 | 3 8 8

8 | 3

As it is mentioned that 2 | 6 equals 26, the data is:

S = {26, 32, 41, 42, 42, 56, 56, 68, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 68, 68, 68, 73, 78, 78, 83}

The data is arranged in ascending order.

The minimum data entry is, 26.

The maximum data entry is, 83.

Answer:

y= 11/19

Step-by-step explanation:

The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.

Given the following information from the table:

Likes running: 28

Does not like running: 46

Column totals: 74

Enjoys swimming: 62

Enjoys cycling: 90

Row totals: 110

The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:

Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)

From the table, the number of students who do not like running and enjoy swimming is given as 46.

Total number of students is given as 74.

Joint relative frequency = 46 / 74

Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.

Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.

In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

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Answer:

3,266.53

Step-by-step explanation:

Rounded to the nearest hundreth thousandths

Answer:

270 degrees

Step-by-step explanation:

There are 60 minutes on a clock face, and the minute hand of a clock makes one complete revolution around the clock face in 60 minutes. This means that the minute hand turns through the angle of 360 degrees in 60 minutes.

The time from 3:30 P.M. to 4:15 P.M. is 45 minutes.

So, during this time, the minute hand of the clock turns through a fraction of a circle equal to:

Fraction of a circle = (angle turned by the minute hand) / (angle for a complete circle)

= (45 minutes) / (60 minutes)

= 3/4

Therefore, the minute hand of the clock turned through 3/4 of a circle during this time.

To find the number of degrees turned by the minute hand, we can multiply the fraction of a circle turned by the total number of degrees in a complete circle:

Degrees turned by the minute hand = (Fraction of a circle turned) x (360 degrees)

= (3/4) x (360 degrees)

= 270 degrees

Therefore, the minute hand of the clock turned through 270 degrees during this time.

The equation of the composite function f(g(x)) is f(g(x)) = 28x^5 - 3 and the interpretation is the amount of money earned when Samantha works for x hours

The functions are given as:

f(x) = 7x^2 - 3

g(x) = √4x^5

To determine the composite function f(g(x)), we have:

f(x) = 7x^2 - 3

Substitute g(x) for x in the above equation f(x) = 7x^2 - 3

f(g(x)) = 7(g(x)^2 - 3

Substitute √4x^5 for g(x) in the above equation f(g(x)) = 7(g(x)^2 - 3

f(g(x)) = 7(√4x^5)^2 - 3

Expand the exponent

f(g(x)) = 7 * 4x^5 - 3

Evaluate the product

f(g(x)) = 28x^5 - 3

Hence, the equation of the composite function f(g(x)) is f(g(x)) = 28x^5 - 3

And the interpretation is the amount of money earned when Samantha works for x hours

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The expected value of the game to you is approximately $0.39.

To calculate the expected value of the game, we need to the probability of winning and losing and the corresponding payoffs.

The probability of drawing two hearts with replacement can be calculated as the product of the probabilities of drawing a heart on the first and second draws.

The probability of drawing a heart from a standard deck of 52 cards is 13/52, as there are 13 hearts out of 52 cards. Since the first card is replaced before the second draw, the probability remains the same for both draws.

Thus, the probability of drawing two hearts is (13/52) * (13/52) = 169/2704.

The payoff for winning is $12, and the payoff for losing is -$1.

To calculate the expected value, we multiply the probability of winning by the payoff for winning and subtract the probability of losing multiplied by the payoff for losing.

Expected Value = (169/2704) * $12 - (2535/2704) * $1 ≈ $0.39.

This means that on average, you can expect to win about 39 cents per game in the long run.

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Answer:

\(Brown = 2400\)

\(Feliz = 3384\)

\(Undecided = 216\)

Step-by-step explanation:

Given

\(N = 6000\) -- population

\(n = 250\) -- sample

From the sample, the proportions are:

\(B = 100\) -- Brown

\(F=141\) -- Feliz

\(U = 9\) -- undecided

Required

Describe the actual population

The actual is calculated using:

\(Actual = \frac{p}{n} * N\)

So, for Brown

\(Brown = \frac{100}{250} *6000\)

\(Brown = \frac{100*6000}{250}\)

\(Brown = \frac{600000}{250}\)

\(Brown = 2400\)

For Feliz

\(Feliz = \frac{141}{250} * 6000\)

\(Feliz = \frac{141* 6000}{250}\)

\(Feliz = \frac{846000}{250}\)

\(Feliz = 3384\)

For undecided

\(Undecided = \frac{9}{250}*6000\)

\(Undecided = \frac{9*6000}{250}\)

\(Undecided = \frac{54000}{250}\)

\(Undecided = 216\)

Answer:

I think the answer to x is 1

Step-by-step explanation:

1 ( x + 6 ) - 3 = 4 ( x + 2 )

1x + 6 - 3 = 4x + 12

          +3          +3

1x + 6 = 4x + 15

    - 6          - 6

1x = 4x + 9

-4x  -4x

-3 = 9

Then divide the -3 with -3 then put an equal sign then put 9 divided by -3.

X = 1

I hope this helps.

Answer:

the answer is

\(x = - \frac{5}{3} \)

Answer:

-8

Step-by-step explanation:

x+2=2(x-1)

_

3

3x+6=2x-2

3x-2x=-2-6

x=-8

Answer:

$7.125

Step-by-step explanation:

1 lb = 16 oz

Cost per ounce

19 / 16 = $1.1875/oz

Cost for 6 oz portion

6 * 1.1875 = $7.125

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Hello there. To solve this question, we'll need to set an easy equation to find how many of each golf ball Paul haves on his bag.

Say the amount of yellow golf balls in his bag is x. It means, according to the question, that he haves 4 times as many white golf balls, such that he haves 4x white golf balls.

The total amount of golf balls he'll have on his bag is x + 4x = 5x.

Now, we know that he haves forty balls in his bag that are either white or yellow.

Making those values equal, we'll get:

5x = 40

Divide both sides of the equation by a factor of 5

x = 8

Paul haves 8 yellow golf balls.

Multiplying both sides by a factor of 4, we'll get the amount of white balls Paul haves:

4*8 = 32.

Paul haves 32 white golf balls on his bag.

Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct