In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is green, DO NOT replace it, and draw another
marble that is yellow?
1
30
O b. 139
OC. 15
45
a.
O d. 7/19
2

The new values for the mean and the standard deviation are 38 and 5 respectively.

The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].

In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.

We let the new population formed be over the variable k.

Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.

Thus, the new mean can be calculated as:

[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]

Thus, the new mean is 38.

Thus, the new standard deviation can be calculated as:

[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]

Thus, the new standard deviation is 5.

Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.

Learn more about the mean and the standard deviation at

https://brainly.com/question/26941429

#SPJ1

Answer:

4 : 9

Step-by-step explanation:

ratio of corresponding sides and ratio of perimeter are equal

then ratio of perimeter = 4 : 9

The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

The complete question is added as an attachment

From the attached figure, we have the following equation

x^4/y = 7

Multiply both sides of the equation by y

x^4 = 7y

The above represents a direct variation from x^4 to y.

Where 7 represents the variation constant

Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

Read more about direct variation at:

https://brainly.com/question/12179965

#SPJ1

Answer: 13 feet

Step-by-step explanation:

Answer:

12.37 ft

Step-by-step explanation:

Hypotenuse(c): the ladder

Cathetus: the wall (a=12) and the floor (b=3)

Equation:

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]

[tex]c^{2} =153[/tex]

[tex]c=\sqrt{153}[/tex]

[tex]c=12.37[/tex]

The ladder is 12.37 feet long

Hope this helps

The equation in function form is f(x)=-4x+80.

What is linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

We can find the equation in function form as shown below:

We have given two points (5,60) and (10,40)

Slope of line

m = (40-60)/ (10-5)

m=-20/5

m=-4

Equation in slope intercept form

(y-y1) =m(x-x1)

(y-60) =-4(x-5)

y-60=-4x+20

y=-4x+20+60

y=-4x+80

y=f(x)

f(x)=-4x+80

Hence, the equation in function form is f(x)=-4x+80.

Learn about Linear function here:

https://brainly.com/question/12983872

#SPJ4

The value of 8√6 as a square root is √384

Surd are written as the square root of prime numbers. Given the expression below;

8√6

This is can be written as;

8√6 = √(8 * 8 * 6)

8√6 = √64 * 6

8√6 = √384

Therefore the value of 8√6 as a square root is √384

learn more on surd function here: https://brainly.com/question/840021

#SPJ1

Answer:

Step-by-step explanation:

The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.

The domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).

The range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).

When the completing the square is applied, the rewritten function is (x + 2)^2 = 4

The equation is given as:

x^2 + 4x = 0

The above equation is a quadratic equation and the coefficient of x in the above equation is 4.

So, we have:

k = 4

Divide the variable k by 2

k/2 = 4/2

k/2 = 2

Square the above result

(k/2)^2 = 4

Next, we add 4 to both sides of x^2 + 4x = 0

x^2 + 4x + 4 = 4

Expand the equation by expressing 4x as 2x + 2x

This gives

x^2 + 2x + 2x + 4 = 4

Factorize the above equation

x(x + 2) + 2(x + 2) = 4

Factor out x + 2 from the above equation

(x + 2)(x + 2) = 4

Rewrite the equation as a perfect square of (x + 2)

(x + 2)^2 = 4

Hence, the rewritten function after completing the square is (x + 2)^2 = 4

Read more about completing the square at:

https://brainly.com/question/4822356

#SPJ1

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

Step-by-step explanation:

Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].

[tex]\textbf{Heya !}[/tex]

basic math tips -»

"of" means multiply

[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]

multiply the numerators and denominators times each other -»

[tex]\sf{\cfrac{5}{10}}[/tex]

reduce:-

[tex]\sf{\cfrac{1}{2}}[/tex]

`hope it was helpful to u ~

Answer: 0.1

Step-by-step explanation:

The smaller the absolute value of the correlation coefficient, the weaker the correlation.

The simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

1) 4 2/7 - 2 1/3

First we convert the mixed fraction 4 2/7 and 2 1/3 into an improper fraction.

4 2/7 = (7×4 + 2 )/7 = 30/7

2 1/3 = (3×2 + 1 )/3 = 7/3

Hence,

30/7 - 7/3

( 30×3 - 7×7  )/21

( 90 - 49  )/21

41/21

2) 4.5 - 2 5/8

First we convert both 4.5 and 2 5/8 into an improper fraction.

4.5 = 4 5/10 = (4×10 + 5)/10 = 45/10 = 9/2

2 5/8 = (2×8 + 5 )/8 = 21/8

Hence,

9/2 - 21/8

(9×8 - 21×2  )/16

(72 - 42  )/16

30/16

15/8

3) 5 2/8 - 15%

First we convert both 5 2/8 and 15% into an improper and proper fraction respectively.

5 2/8 = (5×8 + 2)/8 = 42/8 = 21/4

15% = 15/100 = 3/20

Hence

21/4 - 3/20

(21×20 - 3×4  )/80

(420 - 12  )/80

408/80

51/10

Therefore, the simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

Learn more about fractions here: brainly.com/question/10354322

#SPJ1

Answer:

x=15

Step-by-step explanation:

Use the Pythagorean Theorem: a^2+b^2=c^2

1. a = 20, b = x, c = 25

2. 20^2+b^2= 25^2

3. Expand: 400+b^2= 625

4. Subtract + Simplify: b^2= 625-400

5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225

6. Last Step: Simplify: b = 15.

Here is a similar problem for you to solve, put your answer in the comments.

a= 12, b=5, c=?

Solve for c using the Pythagorean theorem.

Answer:

40%

Step-by-step explanation:

Percent must be equal to 100, so if 60 are girls, then 40% must be boys.

I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS

*TIP: you can delete the answer the second person gave you to be able to recive more answers :)

The surface area of the composite figure is equal to 233.6 square centimeters.

The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:

A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)

A = 233.6 cm²

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

The function is given as:

y = 2x^2 - x - 120

Set the function to 0

2x^2 - x - 120 = 0

Factor out 2

2(x^2 - 0.5x - 60) = 0

Divide by 2

x^2 - 0.5x - 60 = 0

Expand the function

x^2 + 7.5x - 8x - 60 = 0

Factorize the function

(x + 7.5)(x - 8) = 0

Split

x + 7.5 = 0 and x - 8 = 0

Solve for x

x = -7.5 and x = 8

Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

Read more about x-intercepts at:

https://brainly.com/question/3951754

#SPJ1

The individuals in this data set that can be gotten is B) Compression bandage styles and this data set contains A) 3 variables, 1 of which is categorical.

A categorical variables serve as the variable type that posses two or more categories.

This categories could be nominal variable, however considering the data , we can see that the first two are quantitative data and the data are:

THE COMPLETE QUESTION IS:

Alek is taking an inventory of styles of compression bandages for work. Here is the data he has collected.

The individuals in this data set are:Choose 1 answer:

A) Blood Centers

B) Compression bandage styles

C) Nurses

This data set contains:Choose 1 Answer:

A) 3 variables, 1 of which is categorical

B) 3 variables, 3 of which are categorical

C) 6 variables, 1 of which categorical

D) 6 variables, 3 of which are categorical

Learn more about data at:

https://brainly.com/question/17313088

#SPJ1

a.

b.

A quadratic function is a function of the form y = ax² + bx + c

To write y = 5(x - 2)² + 7, we expand the bracket and simplify.

So, y = 5(x - 2)² + 7

y = 5(x² - 4x + 4) + 7

y = 5x² - 20x + 20 + 7

y = 5x² - 20x + 27

So,  the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27

The y intercept is gotten when x = 0.

So, y = 5x² - 20x + 27

y(0) = 5(0)² - 20(0) + 27

y(0) = 0 - 0 + 27

y(0) = 27

The y intercept is (0, 27)

Find the graph in the attachment

To write y = 3(x + 1)² + 12, we expand the bracket and simplify.

So, y = 3(x + 1)² + 12

y = 3(x² + 2x + 1) + 12

y = 3x² + 6x + 3 + 12

y = 3x² + 6x + 15

So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15

The y intercept is gotten when x = 0.

So, y = 3x² + 6x + 15

y(0) = 3(0)² - 6(0) + 15

y(0) = 0 - 0 + 15

y(0) = 15

The y-intercept is (0, 15)

Find the graph in the attachment

Learn more about quadratic function here:

https://brainly.com/question/25841119

#SPJ1

The box-and-whisker plot for the data can be seen in the attachment.

The data given to us is:

50, 51, 54, 55, 57, 61, 62, 63, 65, 66, 67, 68, 71, 71, 76, 76, 77.

As the data is already ordered from least to greatest, we can apply the formulas.

The sample size, n = 17.

Start point = 50.

First quartile, Q1 = (n + 1)/4 th observation = (17 + 1)/4 th observation = 18/4 th observation = 4.5 th observation = average of the 4th and the 5th observation = (55 + 57)/2 = 112/2 = 56.

Median, Q2 = (n + 1)/2 th observation = (17 + 1)/2 th observation = 18/2 th observation = 9th observation = 65.

Third quartile, Q3 = 3(n + 1)/4 th observation = 3(17 + 1)/4 th observation = 3*18/4 th observation = 54/4 th observation = 13.5 th observation = average of the 13th and the 14th observation = (71 + 71)/2 = 142/2 = 71.

End point = 77.

Thus, the box-and-whisker plot should be designed as follows:

The start of the first whisker is from 50, representing the start point.

The start of the box is from 56, representing the first quartile.

The line inside the box is at 65, representing the median.

The end of the box is at 71, representing the third quartile.

The end of the whisker is at 77, representing the endpoint.

The box-and-whisker plot can be seen in the attachment.

Learn more about the box-and-whisker plot at

https://brainly.com/question/28034849

#SPJ1

Answer:

x = 0 , x = 5

Step-by-step explanation:

2x² - 10x = 0 ← factor out 2x from each term on the left side

2x(x - 5) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x - 5 = 0 ⇒ x = 5

Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.

From the given picture we can see the length of the sides. These are 7, 4 and 15.

The length of the two sides cannot join due to the fact that they are less than 15.

4 + 7 < 15

11< 15

Hence the answer is D.

Read more on the triangle theorem here:

https://brainly.com/question/654982

#SPJ1

by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side

Answer:

c

Step-by-step explanation:

option a (x-4) translates the graph 4 units right, not down

option b (x)-4 translates the graph 4 units down, not left

option c (x)+4 translates the graph 4 units up, so it is correct

option d (x+4) translates the graph 4 units left, not right

if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down

if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left