a bag of 16 balls contains one red, three yellow, five green, and seven blue balls. suppose four balls are picked, sampling with replacement. (a) find the probability that the sample contains at least two green balls. (b) find the probability that each of the balls in the sample is a different color. (c) repeat these two problems for the case when the sampling is without replacement.

The equation to represent the number of guests at your party is 150 + 6x = 282 where, the number of guests at the party, x is 22.

Let

Cost of renting a roller rink = $150

Cost per person = $6

Total charge of the party = $282

Number of persons at the birthday party = x

The equation:

150 + 6x = 282

subtract 150 from both sides

6x = 282 - 150

6x = 132

divide both sides by 6

x = 132/6

x = 22

Therefore, there are 22 guests at the birthday party.

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The line of best fit for the given points is y = -1.35x + 9.62, where x is the independent variable and y is the dependent variable. This line represents the linear relationship between the two variables that best fits the given data.

To find the line of best fit for the given points, we can use linear regression. Using a calculator or statistical software, we obtain the following results:

Slope (m) = -1.35

Y-intercept (b) = 9.62

Therefore, the equation of the line of best fit is:

y = -1.35x + 9.62

Rounding to two decimal places, we get:

y = -1.35x + 9.62

The line of best fit for the given points is y = -1.35x + 9.62, which represents the linear relationship between the variables.

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The missing y value in the table can be found to be 19. 5.

To find the missing value, you need to find the relationship that x and y have with each other on the table.

We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:

= 11 - 4                                                 = 9. 5  - 2.5

= 7                                                        = 7

We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.

The y value corresponding to 21 as x would be:

= ( 21 - 15 ) + 13. 5

= 19. 5

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The volume of the solid is the amount of space  value is k = 32.

What is volume in maths?.

Volume in mathematics refers to the quantity of space within a certain 3D object. A fish tank, for example, has measurements of 3 feet long by 1 foot wide and 2 feet high. If you increase the length, breadth, and height by 3x1x2, which is equal to six, you can calculate the volume.

The volume of the solid is represents in cubic units. Thus

     k = ∛v/4

    k³ = v/4

     v = 4k³    ( k≥0)

    when k = 1,  v = 4

  k = z,   v = 4.z³  = 32

 ∴ points (1,1) , (7,32) are on the graph.

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Radius is the distance in a straight line from the centre of the circle to its circumference. The diameter is twice the radius. Therefore,  radius and diameter of the circle are 7 and 14 yards respectively.

The above figure is a circle. The area of the circle is given as 49π yard squared. The question want us to find the radius and diameter of the circle.

Hence,

area of a circle = πr²

where

Therefore,

area of the circle = 49π

Hence,

49π = π × r²

divide both sides by π

r² = 49

square root both sides

r = √49

r = 7 yards

The diameter of a circle is twice the radius.

Hence,

diameter of the circle = 7 × 2 = 14 yards

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Answer:

[tex]\large\boxed{ \sf Area = 25\ ft .^2}[/tex]

Step-by-step explanation:

We need to find out the area of the triangle which has a base of 12.5ft and s height of 4ft.

We know that the formula for calculating the area of the triangle is ,

[tex]\sf:\implies \pink{Area_{\triangle}=\dfrac{1}{2}\times (b)\times (h)}\\[/tex]

where,

F I G U R E : -

[tex] \setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){$\large\bf 4\ ft $}\put(2.8,.3){$\large\bf 12.5\ ft$}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}[/tex]

Now on substituting the respective values, we have;

[tex]\sf:\implies Area = \dfrac{1}{2}\times (12.5) \times (4) \ ft.^2 \\[/tex]

Simplify,

[tex]\sf:\implies \underline{\underline{\boxed{\sf Area = \frak{25\ ft.^2} }}} \\[/tex]

Hence the area of the triangle is 25ft.²

Answer:

Each of the diagonals is 16

Step-by-step explanation:

The diagonals of a rectangular are equal

The two diagonals are QS and RT

QS = RT

→ 30 - 2x = 9 + x

Subtract 30 both sides:
30 - 30 - 2x = 9  -  30 + x

- 2x  = -21  + x

Subtract x both sides
-2x - x = -21 + x  -  x

-3x = -21

x = -21/-3 = 7

So the diagonal RT = 9 + 7 =16

should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16

Part A: The proportion of Iron Bank customers who invest in neither stocks nor futures is 27%.

Part B: Of the Iron Bank customers who invest in futures, 61.54% also invest in stocks.

Part C: The probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%.

Part A:  This can be calculated by subtracting the combined proportion of those who invest in stocks (36%) and those who invest in futures (22%) from 100%.

Part B: This can be calculated by dividing the proportion of those who invest in both stocks and futures (15%) by the proportion of those who invest in futures (22%).

Part C: This can be calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).

Given, that 36% of the customers are investing in stocks and 15% of those customers are also investing in futures.

So, 21% of the customers invest in stocks and not futures, while 79% of the customers either invest in futures, or in neither stocks nor futures.

Therefore, the probability is 21/100, or 18.18%.

In conclusion, the probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%. This is calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).

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Total pay = Regular pay + Overtime pay = $280 + $616 = $896. Therefore, if Lisa works 42 hours in one week, she would be paid $896

The first step is to calculate Lisa's regular pay for the week. We know that her regular hourly rate is $8 per hour. If she works 35 hours or less in a week, then her pay is simply her hourly rate times the number of hours worked. Therefore, her regular pay for a week where she works 35 hours or less would be:

Regular pay = $8/hour * 35 hours = $280

However, we know that Lisa worked 42 hours in one week, which is more than 35 hours. This means she also worked 7 overtime hours. According to the problem, Lisa is paid 11 times her regular salary for any overtime hours worked. This means her overtime pay for the 7 overtime hours would be:

Overtime pay = $8/hour * 11 * 7 hours = $616

To get Lisa's total pay for the week, we simply add her regular pay and overtime pay together:

Total pay = Regular pay + Overtime pay = $280 + $616 = $896

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The other prime factor is even, the number is 30, and its prime factors are 2, 3, and 5.

To find the third prime factor and ultimately the number, we can use the fact that any integer greater than 1 can be expressed as a unique product of prime factors. We know that the number has three prime factors, and two of them are 3 and 5. So, we need to find the third prime factor.

Since the other prime factor is even, it must be 2 (the only even prime number). Therefore, the number can be calculated as:

Number = 3 x 5 x 2 = 30

So, the number is 30, and its prime factors are 2, 3, and 5.

Prime factors are the prime numbers that divide a given number exactly without leaving any remainder. For example, the prime factors of 12 are 2, 2, and 3, because 2 x 2 x 3 = 12 and these are the only prime numbers that divide 12 exactly. To factorize a number into its prime factors, we can use a method called prime factorization. We start by dividing the number by the smallest prime number that divides it exactly. We keep dividing the quotient by the smallest prime number that divides it exactly until we obtain only prime numbers. The prime factors are then the product of these prime numbers

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The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.

Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.

Principal, P = R 8,500

Interest Rate, R = 5%

Time, t = 3 year

Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100

Here, SI = Simple interest

P = Principal (sum of money borrowed)

R = Rate of interest p.a

T = Time (in years)

We have to calculate simpled interest she will have to pay also calculate the total she will pay.

So, Simple interest = (8500×3×5)/100

= 85× 15 = R 1275

Now, total she will have to pay = Principle + SI

= 8500 + 1275

= R 9775

Hence, required total she will pay is R9775.

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The inverse function is [tex]f^{-1} (g) = 10 - g[/tex]

Composition function is a type of function that is formed by combining two or more functions, where the output of one function becomes the input of another function. Composition function shown by the symbol "∘".

The composition function is a mathematical operation that combines two functions to produce a new function. Specifically, given two functions f and g, the composition function (also called function composition) creates a new function h(x) = f(g(x)) that applies the function g to an input x, and then applies the function f to the output of g(x).
We can start by finding the inverse function of f(g), which is [tex]f^{-1} (g)[/tex]. To do so, we need to solve the equation:

[tex]f(g) = x = 10 - g[/tex]

for g, in terms of x:

x = 10 - g

g = 10 - x

This gives us the inverse function:

[tex]f^{-1} (x) = 10 - x[/tex]

Now we can find f^-1(g) by replacing x with g in the above equation:

[tex]f^{-1} (g) = 10 - g[/tex]

Therefore, the function [tex]f^{-1} (g)[/tex] is given by:

[tex]f^{-1} (g) = 10 - g[/tex]

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Complete question is: f:g → 10 - g. Find f-1: g.

Answer:

360°

Step-by-step explanation:

If you travel around the outside of any polygon, the angels will add to 360

Helping in the name of Jesus.

The surface area of the triangular prism is 156.5 inches².

The surface area of a triangular prism can be found as follows:

Therefore, the prism is a triangular prism. The prism has two triangular base with side length 5 inches each. The height of the triangular bases are 4.3 inches each.

The height of the triangular prism is 9 inches. The surface area of the triangular prism is the sum of the whole individual area of each surface of the prism.

Hence,

surface area of the prism = bh + l(s₁ + s₂ + s₃)

Therefore,

surface area of the prism = 4.3 × 5 + 9(5 + 5 + 5)

surface area of the prism = 21.5 + 9(15)

surface area of the prism = 21.5 + 135

surface area of the prism = 156.5 inches²

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The equation of the parabola with focus (4,5) and directrix y=-1 is

[tex](y-5)^2=4(x-4) or (y+1)^2=4(x-4).[/tex]

The equation of a parabola is defined by its focus and directrix. The focus is the point on the parabola that is used to determine its shape, while the directrix is the line used to determine its orientation. The equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex]. This equation can be expressed in terms of the focus and directrix by substituting the x and y values of the focus and directrix into the equation. Substituting the x value of the focus (4) into the equation gives us[tex](y-5)^2=4(4-4)[/tex], which simplifies to[tex](y-5)^2=0[/tex]. This equation can be rearranged to give us y=5, which is the y value of the focus. Substituting the y value of the directrix (-1) into the equation gives us [tex](y+1)^2=4(x-4)[/tex]. This equation can also be rearranged to give us y=-1, which is the y value of the directrix. Therefore, the equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex] or[tex](y+1)^2=4(x-4)[/tex].

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Answer:

the answer is 18

Step-by-step explanation:

volume of triangular prism =l×w×h

9×2×1=18

:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

Answer:Given, csc θ = 3 and θ lies in [0, π/2]We need to find the values of the remaining 5 trigonometric functions.Here is how we can find them:We know that csc θ = 3. csc θ = 1/sin θ. Hence, we can say sin θ = 1/csc θ = 1/3.In the first quadrant, sin θ is positive (All are positive except tan θ and cot θ). Hence, sin θ = 1/3, and cos θ = √(1 - sin²θ) = √(1 - 1/9) = √8/3 = (2/3)√2.The remaining trigonometric functions are:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

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Let's first find the total cost of transportation and admission tickets:

$200 (transportation) + $6.50 (admission ticket) x n (number of students) = $750

$6.50n = $550

n = 84.62

So, the maximum number of students that can go to the game is 84.62. However, we cannot have a fractional number of students, so we can round down to 84 students.

Now, let's find the cost of the meal for each student:

$2.50 (medium sandwich) + $2.00 (drink) + $1.50 (popcorn) = $6.00

If the booster club pays for a large sandwich, drink, and popcorn for each student, the cost will be:

$3.00 (large sandwich) + $2.50 (drink) + $2.00 (popcorn) = $7.50

The difference in cost between the two options is $1.50 per student.

To find how many more students can go to the game with the cheaper meal option, we can divide the total amount of money available ($750) by the difference in cost per student ($1.50):

$750 ÷ $1.50 = 500

So, with the cheaper meal option, the booster club can take 500/6 students = 83 students.

Therefore, the booster club can take 1 more student to the game if they pay for a medium sandwich, drink, and popcorn for each student.

a) An equation in slope-intercept form representing the linear function is y = 12 + 6x.

b) If tomorrow’s practice is 60 minutes long, based on the slope-intercept equation above, the number of drills that Luna's team practice is 8.

The slope-intercept equation is a linear equation in slope-intercept form.

The slope-intercept equation is given as y = mx + b, where:

The number of minutes spent for warm-up practice = 12 minutes

The number of minutes spent per drill = 6 minutes

Let the number of drills per practice = x

Let the total number of minutes spent by the soccer team (length) per practice = y

y = 12 + 6x

The length for tomorrow's practice = 60 minutes

60 = 12 + 6x

60 - 12 = 6x

48 = 6x

x = 8

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Answer:

75%

Step-by-step explanation:

write it as a fraction first, so 15/20.

make the bottom number 100 to get the mark out of 100.

to do this, multiply the bottom by 5 (20x5=100) and then do the same to the top.

you get 75/100. this equals 75%

Answer:

75%

Step-by-step explanation:

In this question, 20 is the highest score you can get on the test so 20 is 100%. We will now want to divide 100 by 20.

100 ÷ 20 = 5

Each score Amore got on the test was worth 5% of the test.

We know he scored 15 on the text, so now we want to multiply 15 with 5.

15 × 5 = 75

Amore scored 75% on his test.

The angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

The 16-notch socket has a cylindrical shape with 16 notches or recesses machined into the interior of the socket. Each notch corresponds to a flat side of a 16-sided nut or bolt head. The notches are evenly spaced around the socket, providing a secure grip on the nut or bolt head and allowing for easy application of torque using a ratchet or wrench.

16-notch sockets are commonly used in automotive and industrial applications, particularly in heavy machinery where large bolts and nuts with 16-sided heads are often used. They are available in a range of sizes to fit different nut and bolt sizes and are typically made of durable materials such as chrome vanadium steel or high-grade aluminum.

Premise 1: Deondra is designing a 16-notch socket wrench.

Premise 2: The notches will be the same size.

Conclusion: Therefore, Deondra needs to know the angle measure for each notch.

To determine the angle measure for each notch, we can use the formula for the interior angle of a regular polygon, which is:

Interior angle = (n-2) x 180 / n

where n is the number of sides (or notches) in the polygon.

Applying this formula to a 16-sided polygon (or hexadecagon), we get:

Interior angle = (16-2) x 180 / 16

Interior angle = 1680 / 16

Interior angle = 105 degrees

Therefore, the angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

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a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.

Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.

Then X follows a binomial distribution with n = 34 and p = 0.6.

a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:

P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:

P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)

= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23

= 0.0332

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:

P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)

= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21

= 0.9876

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:

P(18 <= X <= 24) = P(X <= 24) - P(X < 18)

= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24

- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17

= 0.8782

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Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

[tex]Z=\frac{x-u}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]

u=8.4, sigma=1.8 n=32 s=0.3182

The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:

Z=1.57

Z = 1.57 has a p-value of 0.9418.

1 - 0.9418 = 0.0582.

0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

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Manny's average speed in knots was approximately 11.9 knots. We simply used speed, distance and time formula.

To calculate the average speed in knots, we need to divide the distance sailed in nautical miles by the time taken in hours. So,

Average speed in knots = Distance / Time

Here, the distance is given as 500 nautical miles and the time is given as 42 hours.

Average speed in knots = 500 / 42

= 11.9 (rounded to one decimal place)

Therefore, Manny's average speed in knots was approximately 11.9 knots.

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Answer:

the answer is 7,21

Step-by-step explanation:

To compare the performance of MedStar Washington to other DC-based hospitals on overall satisfaction, we can use the (HCAHPS) survey data available on the Hospital Compare website.

The HCAHPS survey measures patients' perspectives of hospital care, including topics such as communication with doctors and nurses, the responsiveness of hospital staff, cleanliness and quietness of hospital environment, pain management, and medication communication.

To obtain the data for Medstar Washington and other DC-based hospitals (excluding Medstar Georgetown), you can follow these steps:

1) Go to the Hospital Compare website:

2) Click on "Find a Hospital."

3) Enter the city and state of the hospital you want to compare (e.g., Washington, DC) and click "Search."

4) Select "Patient Experience (HCAHPS) Survey" from the "Select a topic" drop-down menu.

5) Click on "Overall Hospital Rating" under the "Survey Summary Star Ratings" section.

6) Select the hospitals you want to compare and click "Compare."

7) You can view the survey results for each hospital on various dimensions of patient experience, such as communication with nurses, communication with doctors, the responsiveness of hospital staff, pain management, cleanliness and quietness, and overall hospital rating.

Based on the data, the administrator of MedStar Washington can identify areas of improvement and take necessary steps to enhance patient satisfaction.

For example, if the hospital is performing poorly in communication with nurses, the administrator can develop programs or training for nurses to improve their communication skills. If the hospital is struggling with pain management, the administrator can work with physicians and nurses to implement best practices and improve pain control.

It's worth noting that Hospital Compare data is based on self-reported patient experience, and other factors such as patient demographics, the severity of illness, and socioeconomic status can influence the scores.

Therefore, the data should be interpreted with caution, and administrators should use multiple sources of information to evaluate the quality of care in their hospitals

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7x ≤ 1, or x ≤ 1/7

(a) The probability that Thomas is selected for the position given that the company’s revenue did not improve is 4 out of 7.
(b) The probability that the company’s revenue will generally improve is the sum of the probabilities that Rachel, Sam and Thomas are hired multiplied by the probability that the company’s revenue will improve given that each individual is hired. This probability is given by (1/7)*(4/5) + (2/7)*(1/2) + (4/7)*(3/10) = 0.5.
(c) For the probabilities given for the second hiring process to be valid, the inequality x + 2x + 4x ≤ 1 must be satisfied. This inequality can be written as 7x ≤ 1, or x ≤ 1/7.

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