You are going to play mini golf. A ball machine that contains 2121 green golf balls, 2424 red golf balls, 2121 blue golf balls, and 1919 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a blue golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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The statements that are true are B and D.

Given are some statements we need to check which is true.

Let's analyze each statement:

A. 4 is a perfect cube.

False. 4 is not a perfect cube because there is no integer that can be cubed to give 4.

B. 16 is a perfect square.

True. 16 is a perfect square because it can be expressed as 4^2, where 4 is an integer.

C. 2,197 is both a perfect square and a perfect cube.

False. 2,197 is not a perfect square because there is no integer that can be squared to give 2,197.

However, it is a perfect cube because 13³ equals 2,197.

D. 8 is a perfect cube.

True. 8 is a perfect cube because it can be expressed as 2³, where 2 is an integer.

E. 18 is neither a perfect square nor a perfect cube.

True. 18 is neither a perfect square nor a perfect cube because there is no integer that can be squared or cubed to give 18.

Therefore, the statements that are true are B and D.

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Step-by-step explanation:

total income=basic salary+commission

=4700+4% of 150000

=4700+6000

total income=10700

Answer:

There are 3 possibilities:

  \(\begin{tabular}{lccc}Alec&7&7&8\\Bryn&18&9&7\\Igor&21&21&24\\Molly&26&17&15\\Suzy&8&26&26\end{tabular}\)

Step-by-step explanation:

This logic puzzle makes use of the relations between numbers and their mean.

__

If two scores in the range of 7 to 26 have a ratio of exactly 3, they must be either 7 and 21, or 8 and 24. In order for the mean to be exactly 16, the total of the 5 scores must be 5×16 = 80.

If the 3:1 range involves scores of 21 and 7, then we know ...

  Alec got 7

  Igor got 21

The total of these and the score of 26 is 54. The remaining two scores must total 80-54 = 26. We know that there must be two scores that have a difference of 8, so there are two possibilities:

  Molly got 26 and Bryn got 18, leaving Suzy with a score of 8.

  Molly got 17 and Bryn got 9, leaving Suzy with a score of 26.

The possibilities here are ...

  Alec 7, Bryn 18, Igor 21, Molly 26, Suzy 8

  Alec 7, Bryn 9, Igor 21, Molly 17, Suzy 26

If the 3:1 range involves scores of 24 and 8, then we know ...

  Alec got 8

  Igor got 24

The total of these and the score of 26 is 58. The remaining two scores must total 80-58 = 22. That two scores have a difference of 8 leaves open one possibility: the remaining two scores are 7 and 15. (If one were 18=26-8, the other would be 22-18=4, too low for the given range.)

  Alec 8, Bryn 7, Igor 24, Molly 15, Suzy 26

___

Possible marks are ...

  \(\begin{tabular}{lccc}Alec&7&7&8\\Bryn&18&9&7\\Igor&21&21&24\\Molly&26&17&15\\Suzy&8&26&26\end{tabular}\)

_____
Additional comment

When two numbers are required to have a specific sum (s) and a specific difference (d), the two numbers are (s+d)/2 and (s-d)/2.

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square

In order to get the shape using the vertices that we have, we would have to find the length of the diagonals

We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)

The length of the diagonal PQ is given as:

PQ = \(\sqrt{(0-4)^2+(4-0)^2}\)

= \(\sqrt{32}\)

Next we have to solve for the length of the diagonal RS

RS = \(\sqrt{(4-(-4))^2+(0-(-4))^2\)

RS = \(\sqrt{32}\)

Since PQ = RS we would have to conclude that the shape is a square.

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Answer:

D.

Step-by-step explanation:

6a² = surface area for cube

6(5)² = 150

2\(\pi\)(r)(h)+2\(\pi\)r²  = surface area cylinder

2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi

150 + 20pi = 212.8318531

The amount after 5 years on $100 using the compound interest is $122.

According to the question,

We have the following information:

Principal = $100

Interest Rate = 4%

Time= 5 years

We know that the following formula is used to find the total amount if there is compound interest:

Compound amount = \(P(1+\frac{r}{100})^{t}\) where P is the principal, r is interest rate and t is the time in years

(Note that there are different formulas for compound interest depending on how it is calculated.)

A = \(100(1+\frac{4}{100})^{5}\)

A = \(100(\frac{104}{100})^{5}\\100(1.04})^{5}\)

A = 100*1.22

A = $122

Hence, the amount after 5 years on $100 using the compound interest is $122.

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Answer:

x = 3

y = -5

Step-by-step explanation:

       4x + y = 7 -------------------(I)

       5x - y = 20 -----------------(II)

Add both the equations. Now, y will be eliminated, and we can find the value of 'x'.

       (I)           4x + y = 7

      (II)           5x - y = 20       {Add the equations}

                    9x       = 27

Divide both sides by 9,

                            x = 27 ÷ 9

                            \(\boxed{\bf x = 3}\)

Now, Plugin the value of 'x' in equation (I)

          4*3 + y = 7

           12 +  y = 7

Subtract 12 from both sides,

                    y = 7 - 12

                    \(\boxed{\bf y = -5}\)

Answer:

-9

Step-by-step explanation:

Plug it in

g(x)=-x-4

g(5) meaning that x=5

Thus,

-5-4=-9

Hope it find it helpful :)

Answer:

-1

Step-by-step explanation:

Given g(x) = -x + 4, find g(5)

g(x) = -x+4

g(5) = -(5) + 4          Plug input into x

-5 + 4                       Negate

-1                              Add

Answer:

3

Step-by-step explanation:

x − (y − y)

3-(6-6)

3-0

3

Step-by-step explanation:

Given

x = 3 and y = 6 Then

x - (y-y)

= 3 - ( 6 - 6 )

= 3

Hope it will help :)

Answer:

18

Step-by-step explanation:

\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)

Answer:

The value is 20.

Step-by-step explanation:

To solve this equation, you must use the method of PEMDAS.  In this order, you should multiply 8 by 2 first to get 16 for the first part of your answer.  Your equation should now be 7 + 16 - 6 + 3.  You can now solve this equation from left to right manually.  Add 16 from 7 to get 23, subtract 6 from that number to get 17 and add 3 to get your final answer which is 20.

Answer:

27 :)

Step-by-step explanation:

7+8=15

15x2=30

30-6=24

24+3=27

Answer:

d

Step-by-step explanation:

The inverse operation would be to multiply it by 3, missing value is 12

Answer:

3748096

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

Just add the right side. 40 + 15

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Answer:

In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.

Here is one way to find the values of k and m in a parallelogram:

Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.

Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let the slope of AB be represented by k.

Find the slope of the line segment AD by using the same formula and let it be represented by m.

The values of k and m are now found.

Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.

It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.

Step-by-step explanation:

Answer:180 u

Step-by-step explanation:

Answer:

Step-by-step explanation:

Well you have 1/2 the answer.

m = 7/3

y = mx + b

y = 7/3 * x + b

Use the point to to determine b

x = -5

y = 8

8 = 7/3 * (-5) + b

8 = -35/3 + b           Add 35/3 to both sides

8 + 35/3 = b

19 2/3 = b

So the complete answer is

y = 7/3 x + 19 2/3

Answer:

Answer: 630

Step-by-step explanation: 18 feet tall is the gateway arch . The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St

Answer:

Step-by-step explanation:

Multiplying decimals is not as hard as you think :)

Example 1:

Multiply: 5.2 x 4.5

Step #1: Line up the decimals

Step #2: Multiply like you usually would when multiplying two numbers.

Step #3: Move your decimal twice to the left to get 23.40

Work:

  5.2

x 4.5

 260

+ 2080

 23.40 (I moved the decimal twice to the left from the zero)

Answer:

Step-by-step explanation:

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

profits will increase so with that being said the supply of them dropped if demand increased getting bikes will be harder for competing business in the area and so therefore if you have 200 bikes and others have 50 bikes your gonna make way more profit and for the people with 50 bikes they will gain and lose profits because when they run out of bikes they have to buy more and they are more expensive because of the demand on them

Step-by-step explanation:

The explanation regarding the change of price that impact the profits should be explained below.

The profit should rise when the supply should fall. In the case when I have 200 bikes while the other should have 50 bikes so here I make more profit however the other people will gain but the profit should be lost since the bikes should be out of the stock and at the same time they need to buy more that should be more expensive due to the demand.

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Answer:

Step-by-step explanation: m=s-c/c

Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

A. The zeroes are -3 and -2/3 because y= (x + 3) (3x + 2)

Step-by-step explanation:

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12