In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.

Answers

Answer 1

Answer:

The expected number of winning balls that Heather draws is 0.3.

Step-by-step explanation:

The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Expected value of the hypergeometric distribution:

The expected value is given by:

[tex]E(X) = \frac{nk}{N}[/tex]

Expected number of blue and green balls:

40 balls, which means that [tex]N = 40[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

25 are blue, which means that [tex]k = 25[/tex]

So

[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]

1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.

Of the blue balls, 12% are winning.

Of the green balls, 20% are winning.

Calculate the expected number of winning balls that Heather draws.

[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]

The expected number of winning balls that Heather draws is 0.3.


Related Questions

if the mean of a random variable X is 45 what will be the mean of the sampling distribution of the sample mean?

Answers

Answer:

The mean of the sampling distribution is always equal to the mean of the population.

The mean of the sampling distribution of the sample mean is 45.

Given that,

The mean of the random variable X is 45.We need to find out the mean of the sampling distribution.

Based on the above information, the calculation is as follows:

= mean of the random variable X

= 45

As the sampling distribution mean should always be equivalent to the population mean.

Therefore we can conclude that the mean of the sampling distribution of the sample mean is 45.

Learn more: brainly.com/question/521501

The of the matrix whose columns are vectors which define the sides of a parallelogram one another is the area of the parallelogram?

Answers

Answer:

absolute value of the determinant, adjacent to, equal to

Step-by-step explanation:

The absolute value of a determinant  of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to  one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].

The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:


Month Machine Hours Electricity Costs
January 2,300 $ 19,100
February 2,700 $ 22,400
March 1,700 $ 14,200
April 2,900 $ 24,400
May 3,600 $ 28,950
June 3,100 $ 23,400
July 3,900 $ 25,450
August 3,300 $ 23,450
September 1,800 $ 16,900
October 3,500 $ 27,400
November 4,500 $ 32,400
December 4,000 $ 28,450


Summary Output
Regression Statistics
Multiple R 0.957
R Square 0.917
Adjusted R2 0.908
Standard Error 1,586.26
Observations 12.00


Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 5,970.52 1,766.77 3.38 0.01 2,033.90 9,907.13
Machine Hours 5.76 0.55 10.49 0.00 4.54 6.98

The percent of the total variance that can be explained by the regression is:

Answers

Answer:

0.924

Step-by-step explanation:

R² = 0.854

R = √0.854

R = 0.924

Hence, the correlation Coefficient of electricity tarrif is 0.924 ; this correlation Coefficient value, depicts a strong positive correlation between machine hours and cost of electricity. And can he interpreted to mean that ; Electricity tarrif increases as machine hours increases and also decreases as machine hours decreases.

In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice. ​

Answers

9514 1404 393

Answer:

  5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.


What are the roots of the polynomial equation x3 - 6x= 3x2 - 8? Use a graphing calculator and a system of equations

Answers

Answer:

Hence, the roots of the polynomial equation are:

-2, 1, 4

Step-by-step explanation:

We are asked to find the roots of the polynomial equation:

We can also equate this equation to y to obtain a system of equation as:

and

Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.

Hence, the point of intersection of the two graphs are:

(-2,4), (1,-5) and (4,40)

Hence, the roots of the polynomial equation are:

-2, 1, 4

How can you use transformations to graph this function?

Answers

Answer:

What function?

Step-by-step explanation:

SCALCET8 3.9.017.MI. Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later

Answers

Answer:

The rate at which the distance between the cars increasing two hours later=52mi/h

Step-by-step explanation:

Let

Speed of one car, x'=48 mi/h

Speed of other car, y'=20 mi/h

We have to find the rate at which the distance between the cars increasing two hours later.

After 2 hours,

Distance traveled by one car

[tex]x=48\times 2=96 mi[/tex]

Using the formula

[tex]Distance=Time\times speed[/tex]

Distance traveled by other car

[tex]y=20\times 2=40 mi[/tex]

Let z be the distance between two cars after 2 hours later

[tex]z=\sqrt{x^2+y^2}[/tex]

Substitute the values

[tex]z=\sqrt{(96)^2+(40)^2}[/tex]

z=104 mi

Now,

[tex]z^2=x^2+y^2[/tex]

Differentiate w.r.t t

[tex]2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}[/tex]

[tex]z\frac{dz}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}[/tex]

Substitute the values

[tex]104\frac{dz}{dt}=96\times 48+40\times 20[/tex]

[tex]\frac{dz}{dt}=\frac{96\times 48+40\times 20}{104}[/tex]

[tex]\frac{dz}{dt}=52mi/h[/tex]

Hence, the rate at which the distance between the cars increasing two hours later=52mi/h

The alternative hypothesis for a two-tailed test of a single population proportion might be?

A. Ha: P>0.4

B. Ha: P< 0.4

C. Ha: p~=0.4 (~means not equal to)

Answers

Answer:

tgis moght help

Step-by-step explanation:

https://opentextbc.ca/introbusinessstatopenstax/chapter/full-hypothesis-test-examples/

help me pleaseeeeeeeeeeeeeeeeee………….

Answers

Answer:

C

Step-by-step explanation:

200 x 5 = 1,000

100 x 10 = 1,000

C - 5 to 10 days

Answer:

C. 5 to 10 days

Step-by-step explanation:

If she drove 100 miles per day, then

1000/100 = 10

it took her 10 days.

If she drove 200 miles per day, then

1000/200 = 5

it took her 5 days.

Since she drove between 100 miles and 200 miles per days,

it took her from 5 to 10 days.

Answer: C. 5 to 10 days

Express each ratio as a fraction in its lowest terms.
18 hours to 2 days​

Answers

Answer:

3/8.

Step-by-step explanation:

First convert days to hours:

2 days = 2 * 24 = 48 hours.

The greatest common factor of 18 and 48 = 6 so the required fraction is

18/48

= (18/6) / (48/6)

= 3/8.

Althea has $100. She divides it evenly among her 4 children. Her oldest child, Raul, spends $15 of the amount he receives. How much money does Raul have left after he spends $15?

Which statements about this word problem are true? Check all that apply.

This is an example of a part-whole problem.
This is an example of a comparison problem.
Addition then multiplication can be used to solve the problem.
Division then subtraction can be used to solve the problem.
Division then multiplication can be used to solve the problem.

Answers

Step-by-step explanation:

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

Division then subtraction can be used to solve the problem.

What is mathematical expressions?

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Given

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

to learn more about mathematical expressions refer to:

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uppose that the walking step lengths of adult males are normally distributed with a mean of 2.8 feet and a standard deviation of 0.2 feet. A sample of 76 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 2.5 feet. Round your answer to 4 decimal places, if necessary.

Answers

Answer:

.0668

Step-by-step explanation:

Formula:

z=(x-average)/standard deviation

(2.5-2.8)/.2= -1.5

Go to a ztable and find the value for 1.5  (.9332) and take the compliment of this (we can do this because the normal distribution is symmetrical)

1-.9332= .0668

Given the function
Calculate the following values:

Answers

Answer:

f(-1) = 1

f(0) = 20

f(2) = 38

Step-by-step explanation:

f(-1) = 9×-1 + 10 = -9 + 10 = 1

f(0) = 9×0 + 20 = 0 + 20 = 20

f(2) = 9×2 + 20 = 18 + 20 = 38

we needed to use the second definition for f(0), because that is the same as saying x=0.

and that is in the domain of the second function definition ( x>=0).

Given right angle ABC, what the value of tan(A)?
5/13
12/13
12/5
13/12
need answer asap

Answers

Hi there!

[tex]\large\boxed{12/5}}[/tex]

tan (angle) = Opposite side / Adjacent side, so:

Tan (A) = opposite side / adjacent side

= 24 / 10

Simplify:

= 12 / 5


Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was & miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.

Answers

Answer:

(1) +t+=+1.2+ hrs

Step-by-step explanation:

Two methods, A and B, are available for teaching Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:

A—Method A is used.
B—Method B is used.
L—Spanish was learned successfully. A person learned Spanish successfully.

What is the probability that he was taught by method A?

Answers

Answer:

0.7671 = 76.71% probability that he was taught by method A

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Person learned Spanish successfully.

Event B: Method A was used.

Probability of a person learning Spanish successfully:

70% of 80%(using method A)

85% of 20%(using method B)

So

[tex]P(A) = 0.7*0.8 + 0.85*0.2 = 0.73[/tex]

Probability of a person learning Spanish successfully and using method A:

70% of 80%, so:

[tex]P(A \cap B) = 0.7*0.8 = 0.56[/tex]

What is the probability that he was taught by method A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.56}{0.73} = 0.7671[/tex]

0.7671 = 76.71% probability that he was taught by method A

Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fractions where needed.)

Answers

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

[tex]a = 2i + j -3k[/tex]

[tex]b = 3i - 2j -k[/tex]

Required

The angle between them

The cosine of the angle between them is:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

First, calculate a.b

[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]

Multiply the coefficients of like terms

[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]

[tex]a \cdot b =7[/tex]

Next, calculate |a| and |b|

[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]

[tex]|a| = \sqrt{14[/tex]

[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]

[tex]|b| = \sqrt{14}[/tex]

Recall that:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

This gives:

[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]

[tex]\cos(\theta) = \frac{7}{14}[/tex]

[tex]\cos(\theta) = 0.5[/tex]

Take arccos of both sides

[tex]\theta =\cos^{-1}(0.5)[/tex]

[tex]\theta =60^o[/tex]

Estimate 19.625-6.77 by first rounding each number to the nearest tenth.

Answers

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

Which of the following is true?

Answers

Answer:

Step-by-step explanation:

A=45

The answer to this 6th grade summer school math question is

Answer 7.84

Answers

7.84
Steps on how I solved it
2.8x2.8= 7.8

A shopkeeper supplies 42 kg of vegetables to a school canteen in the morning and 58 kg of vegetables in the evening if cost of 1kg vegetable is 16 rupees how much money is due to the canteen per day?​

Answers

1,600 rupees

Add both instances of supplying vegetables in 1 day together.

42 kilograms + 58 kilograms = 100 kilograms

Since each kilogram of vegetables equals 16 rupees, 100 kilograms of vegetables is just this number multiplied by 100.

16 rupees * 100 = 1600 rupees

You need
1
1
4
feet of string to make 20 holiday ornaments.

To make 14 holiday ornaments, you will need
feet of string.

Answers

Answer:

79.8

Step-by-step explanation:

math

help me please i am struggle with this

Answers

The Answer is H I solved it out

3.
Salary: A sales clerk receives a monthly
salary of $500 plus a commission of 6% on all
sales over $3500. What did the clerk earn the
month she sold $8000 in merchandise?

Answers

Answer:

Step-by-step explanation:

I  might be wrong but it 1900 in merchandise

The clerk earned a total of $770 for the month she sold $8000 in merchandise.

To calculate the clerk's earnings for the month she sold $8000 in merchandise, we need to consider her monthly salary and commission.

The clerk's monthly salary is $500, which is a fixed amount.

For the commission, we need to calculate the sales amount that exceeds $3500. In this case, the sales amount exceeding $3500 is $8000 - $3500 = $4500.

The commission is calculated as 6% of the sales amount exceeding $3500. Therefore, the commission earned by the clerk is 6% of $4500.

Commission = 6/100 * $4500

Commission = $270

Adding the monthly salary and commission, we can calculate the clerk's total earnings for the month:

Total earnings = Monthly salary + Commission

Total earnings = $500 + $270

Total earnings = $770

Therefore, the clerk earned a total of $770 for the month she sold $8000 in merchandise.

To know more about  merchandise. here

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In the coordinate plane, two vertices of square ABCD are A (0,0) and B (0, m). What are the coordinates of points C and D? Do not introduce any new variables.​

Answers

Answer:

Step-by-step explanation:

As shown in the graph,

A, B, C and D are the vertices of a square, all sides of the square will be equal in measure.

Coordinates of A → (0, 0)

Coordinates of B → (0, m)

Distance between point D and point A = m

Therefore, coordinates of point D → (m, 0)

Now point C will be equally distant from the points B and D.

Coordinates of C → (m, m)

The endpoints of PC are P(4, 1) and Q(4,8). Find the midpoint of PQ
A. (4, 4.5)
B. (0, -3.5)
C. (4.5, 4)
D. (6, 3.5)

Answers

Answer:

A. (4,4.5)

Step-by-step explanation:

Midpoint={x1+x2/2,y1+y2/2}

M={4+4/2,1+8/2}

M={8/2,9/2}

M={4,4.5}

NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?

4. Suppose y varies inversely with the x, and y = -1 when = 3. What inverse variation equation relates x and y?

a. y = 3/x
b. b. y = -3x
c. y = 3x
d. y = -3/x

5. Suppose y varies inversely with x and y = 68 when x = 1/17. What is the value of x when y = 16?

a. 64
b. 32
c. 1/4
d. 1/16

6. Suppose y varies inversely with x, and y = 5 when x = 15. What is the value of y when x = 25
a. 3
b. 5
c. 25
d. 15

Answers

Answer:

4,a

5.d

6.c

plz mark me as brainliest

Step-by-step explanation:

Answer:

1. A

2. C

3. A

Step-by-step explanation:

all the explanations are In the image above

The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 41 hours. A single plant operates three galvanizing lines that are assumed to operate independently. Round your answers to four decimal places (e.g. 98.7654).
(a) What is the probability that none of the lines experiences a surface finish problem in 41 hours of operation?
(b) What is the probability that all three lines experience a surface finish problem between 24 and 41 hours of operation?

Answers

Answer:

a) The probability that none of the lines experiences a surface finish problem in 41 hours of operation is 0.0498.

b)The probability that all three lines experience a surface finish problem between 24 and 41 hours of operation is 0.0346.

Step-by-step explanation:

[tex]Mean = \frac{1}{\lambda} = 41\\P(X\leq x)= 1-e^{-\lambda x}[/tex]

[tex]P(X>x)= e^{-\lambda x}[/tex]

a)

[tex]P(x> 41, y>41, Z>41) = (P(X>41))^{3}\\\\P(X>41)=e^{^{-\frac{41}{41}}}=e^{-1}[/tex]

[tex]P(x> 41, y>41, Z>41) = \left (e^{-1} \right )^{3}\\\\P(x> 41, y>41, Z>41) = e^{-3} = 0.0498.[/tex]

b)

[tex]\lambda =\frac{24}{41}\\P(X=1)=e^{-\lambda }\cdot \lambda =\left ( e^{-0.585} \right )\left ( 0.585 \right )\\P(X=1)=0.326[/tex]

For 3 where, P(X=1, Y==1, Z=1)

                     [tex]= (0.326)^{3} \\\\= 0.0346[/tex]

A paper weight is made in the shape of a triangular pyramid.The dimensions of the paper weight are shown The formula for the volume of a triangular pyramid is V = 1/3 Bh .Which expression can be usef to find the value of B the area of the base of the pyramid

Answers

Answer:

[tex]B = \frac{3V}{h}[/tex]

Step-by-step explanation:

Given

[tex]V = \frac{1}{3}Bh[/tex]

Required

Solve for B

We have;

[tex]V = \frac{1}{3}Bh[/tex]

Multiply by 3

[tex]3V = Bh[/tex]

Make B the subject

[tex]B = \frac{3V}{h}[/tex]

If f(x) is a linear function, what is the value of n?
х
_4
f(x)
---25
-10
-1
n
20
2
оооо
9

Answers

Step-by-step explanation:

You can simply plot these points on a graph and see where the line goes. It go

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