Suppose the composition of the 107th Senate is 45 Republicans, 50 Democrats, and 5 Independents. A new committee is being formed to study ways to benefit the arts in education. If 3 senators are selected at random to head the committee, find the probability of the following:
Part 1. The group of 3 consists of all Republicans.
Part 2. The group of 3 consists of all Democrats.
Part 3. The group of 3 consists of 1 from each party, including the Independent.

Answers

Answer 1

Answer:

1 : 0.088

2 : 0.12

3 : 0.07

Step-by-step explanation:

45 Rebullicans

50 Democrats

5 independents

Total = 100

Selection =  3

Part 1:

(45 C 3) / (100 C 3) = 0.088

Part 2:

(50 C 3) / (100 C 3) = 0.12

Part 3:

(45 C 1) x (50 C 1) x (5 C 1) / (100  C 3) = 0.07


Related Questions

PLEASE HELP

A spinner is divided into eight equal sections numbered 1-8. find the probability of not spinning a 5. write your answer as a fraction, percent and decimal.

Answers

Answer:

7/8, 87.5%, 0.875

Step-by-step explanation:

There is only 1 5 on the spinner. And there are 8 equal sections.

The probability of spinning a 5 is 1/8.

So, the probability of not spinning a 5 is 7/8

To find the Percent and Decimal form, divide 7 by 8.

You get 0.875-the decimal form

Move the decimal point 2 places to the right:

87.5

Add the percent symbol, and you're done!

I hope this helps!

Tell me if you need more explaining :)

Land costing $140,000 was sold for $173,000 cash. The gain on the sale was reported on the income statement as other income. On the statement of cash flows, what amount should be reported as an investing activity from the sale of land?

Answers

Answer:

Amount should be reported in investing activities = $173,000

Step-by-step explanation:

Given:

Amount of land costing = $140,000

Sold amount of land = $173,000

Find:

Amount should be reported in investing activities

Computation:

Amount should be reported in investing activities = $173,000

The cash flow statement shows how much money is coming in and going out. The whole amount of cash received, which is 173,000 dollars, will be recorded as proceeds from the sale of land in the investment activity. As a result, the right answer is 173,000.

Look at photo help please I will give brainliest

Answers

Answer:

3x² + 13x + 4

Step-by-step explanation:

I did the steps in my book

a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches. Find the angle between the diagonal of the box and the diagonal of its base. The angle should be measured in radiands

Answers

Answer:

0.7246 radians

Step-by-step explanation:

According to the Question,

Given that, a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches

The length of the base diagonal (d) can be found using the Pythagorean theorem on length and width:

d = √{ (12)² +(15)² }  = √(144+225) = √369inches

The tangent of the angle is the ratio of the height of the box to this length

 Tan∅ = 17/√369

Taking the [tex]Tan^{-1}[/tex] , we have

∅ = [tex]Tan^{-1}[/tex](17/√369) ≈ 0.7246 radians

For any number n>1, is
|(.5 +.2i)^n|
A. greater than 1?
B. less than 1?
C. equal to 1?
PLZ HELP

Answers

Answer:

B. Less than 1

Step-by-step explanation:

You could plug in values of n greater than 1 and see what happens....

Example n=2 gives |(.5+.2i)^2|

Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|

=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.

Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29

This value is less than 1.

We should also be able to do the absolute value first then the power.

|.5+.2i|=sqrt(.25+.04)=sqrt(.29)

So |.5+.2i|^2=.29 which is what we got long way around.

Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.

Jose bought 217 shares of Darien Electric for $21.96 apiece. His broker charged him a commission of $106.12 for the
purchase. If the yearly dividend on Darien Electric is 77 cents per share, what is the annual yield on Jose's stock? Show
work.

Answers

Answer:

what is photosynthic ..

p.l.e.a.s.e join eti-fgdd-xjs

why do plant need it

Need help on the last problem please.

Answers

Answer:

6 of x and 5 of y

Step-by-step explanation:

x = number of closets of the first type

y = number of closets of the second type

1200 = 100x + 120y

100 = 10x + 8y

10x = 100 - 8y

10x(100 - 8y) + 120y = 1200

1000 - 80y + 120y = 1200

40y = 200

y = 5

100 = 10x + 8×5 = 10x + 40

60 = 10x

x = 6

20x + 24y = max

20×6 + 24×5 = 120 + 120 = 240

Anyone know this question?

Answers

‘All of these’

F(x) is the same as saying y

Let me know

Write the equation of the line that passes through the points ( – 3, 2) and ( - 1,6).

Answers

Answer:

the answer is y=2x+8

Step-by-step explanation:

Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm’s three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $15 for David, and $18 for Sarah.Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)

Answers

Answer:

a) Minimize Z =30 X1 +25 X2+18 X3

subject to following constraints

[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]

b) Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.

c) As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.

Step-by-step explanation:  

Step 1:-

a)  

Let's take  

X1 to be the number of hours assigned to Lisa  

X2 to be the number of hours assigned to David  

X3 to be the number of hours assigned to Sarah.  

The objective function is to attenuate the entire cost of the project by deciding an optimum number of hours for every person. the target function is given by -  

Minimize Z =30 X1 +25 X2+18 X3

subject to following constraints

[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]  

Constraints and explanation:  

1. Lisa must be assigned a minimum of 40% of the entire number of hours assigned to the 2 senior designers.  

2. Sarah must be assigned a minimum of 15% of the entire project time.  

3. The corporate estimates that 150 hours are going to be required to finish the project.  

4. The number of hours assigned to Sarah must not exceed 25% of the entire number of hours assigned to the 2 senior designers.  

5. Lisa features a maximum of fifty hours available to figure on this project.  

6. Non-negative condition.  

Step 2:-  

b)

From the above equations, we get  

The number of hours assigned to Lisa is 48 hours  

The number of hours assigned to David 72 hours  

The number of hours assigned to Sarah 30 hours.  

Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.  

Step 3:-

c)  

As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.

Jonas builds a snow fort. He tells his friends it is 0.8 meters tall inside, but he rounded the height to the nearest tenth.
Which could be the height of the snow fort before Jonas rounded it?
2 answers
A. 0.85
B. 0.82
C. 077

Answers

Answer:

B. 0.82

C. 077

Step-by-step explanation:

Given

[tex]Number = 0.8[/tex] -- approximated

Required

The possible value of Number

Since [tex]Number = 0.8[/tex] is approximated, then the possible values of Number that  can be gotten from the preparation

The approximated value 0.8 has the following range: 0.75 to 0.84

Options B and C are in this category.

Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level. The null and alternative hypothesis would be: H 0 : p N ≥ p D H 1 : p N < p D H 0 : p N ≤ p D H 1 : p N > p D H 0 : p N = p D H 1 : p N ≠ p D H 0 : μ N ≤ μ D H 1 : μ N > μ D H 0 : μ N ≥ μ D H 1 : μ N < μ D H 0 : μ N = μ D H 1 : μ N ≠ μ D The test is: two-tailed right-tailed left-tailed The sample consisted of 30 night students, with a sample mean GPA of 3.34 and a standard deviation of 0.02, and 30 day students, with a sample mean GPA of 3.32 and a standard deviation of 0.08. The test statistic is: (to 2 decimals) Use the conservative degree of freedoms. The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Answers

Answer:

H0 : μN ≤ μD

H1 : μN > μD

Right tailed

Test statistic = 1.33

Pvalue = 0.097

Fail to reject the Null

Step-by-step explanation:

H0 : μN ≤ μD

H1 : μN > μD

The test is right tailed ; culled from the direction of the greater than sign ">"

Night students :

n1 =30 x1= 3.34 s1 = 0.02

Day students:

n2 = 30 x2 = 3.32 s2 = 0.08

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

T= (3.34 - 3.32) / √(0.02²/30) + (0.08²/30)

T = 0.02 / 0.0150554

Test statistic = 1.328

Using the conservative approach ;

df = Smaller of n1 - 1 or n2 - 1

df = 30 - 1 = 29

Pvalue(1.328, 29) = 0.097

At α = 0.10

Pvalue < α ; Hence, we reject H0 ; and conclude that there is significant evidence that GPA of night student is greater than GPA of day student

Help me write this as an absolute value function!

Answers

Answer:13

Step-by-step explanation:11

The Sureset Concrete Company produces concrete. Two ingredients in concrete are sand (costs $6 per ton) and gravel (costs $8 per ton). Sand and gravel together must make up exactly 75% of the weight of the concrete. Also, no more than 40% of the concrete can be sand and at least 30% of the concrete be gravel. Each day 2000 tons of concrete are produced. To minimize costs, how many tons of gravel and sand should be purchased each day

Answers

Answer:

The Sureset Concrete Company

The tons of gravel and sand that should be purchased each day are:

Sand = 800 tons

Gravel = 700 tons

Step-by-step explanation:

Two ingredients for producing concrete = sand and gravel

Cost of sand per ton = $6

Cost of gravel per ton = $8

Sand and gravel = 75% of the concrete

Therefore 25% (100 - 75%) will be made up of cement and water

Tons of concrete produced each day = 2,000

Sand and gravel = 1,500 (2,000 * 75%)

Sand <= 40% of 2,000 = 800 tons

Gravel => 30% of 2,000 = 700 (1,500 - 800) tons

To minimize costs,  800 tons of gravel and 700 tons of sand should be purchased each day.

Total cost incurred daily for both sand and gravel = $10,400 (800 * $6 + 700 * $8)

Please show process!!!!
THANK YOU!
Will mark brainylist

Answers

Answer: 103 degrees

Step-by-step explanation:

51 + 26 = 77

A triangle adds up to 180 degrees

180 - 77 = 103

= 103 degrees

what much is 1/2 - 1/4

Answers

Answer:

1/4

Step-by-step explanation:

The answer is 1/4.

1/2 is equivalent to 2/4.

2/4-1/4=1/4

1/4 + 1/4 is 1/2 , so think of it as 2+2 =4. If you subtract 4 from 2, you will get 2. So 1/2-1/4 is 1/4

Please guys help to solve this problem​

Answers

9514 1404 393

Answer:

  300

Step-by-step explanation:

Since nobody failed, the number who passed one or the other was 100%.

  P(O + W) = P(O) +P(W) -P(O&W)

  100% = 80% +70% -P(O&W)

  P(O&W) = 50% = 150 students

If 150 students are 50% of the examinees, then 100% will be 300 students.

Answer:

[tex]300[/tex]

hope it helps

#CARRYONLEARNING

g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19

Answers

Answer:

[tex]241^{257}\ mod\ 12 =1[/tex]

[tex]7 * 20 = 140[/tex]

[tex]\frac{1}{700}[/tex]

Step-by-step explanation:

Solving (a): 241^257 mod 12

To do this, we simply calculate [tex]241\ mod\ 12[/tex]

Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]

The highest number less than or equal to 241 that is divisible by 12 is 240; So:

[tex]241\ mod\ 12 = 241- 240[/tex]

[tex]241\ mod\ 12 =1[/tex]

Hence:

[tex]241^{257}\ mod\ 12 =1[/tex]

Solving (b): 7 * 20

[tex]7 * 20 = 140[/tex]

Solving (c): Multiplicative inverse of 7 in 719

The position of 7 in 719 is 700

So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number

what is 1.8 in written notation

Answers

Answer:

The answer is 1/8

write the following in set builder form C={1,4,9,16,25}​

Answers

Answer:

C={n : n=i^2 where i belongs to Natural_numbers and 1 <= i <= 5}

Given the points (-7, -1) and (8, 5) find the slope.

Answers

Answer:

(-7, -1) =(x1,y1)

(8, 5)=(x2,y2)

now

[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]

[tex]or = \frac{5 + 1} {8 + 7} [/tex]

[tex]or = \frac{6}{15} [/tex]

[tex]or = \frac{2}{5} [/tex]

Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you ☺️

Calculate 20% of 15,998

Answers

Answer:

3,199 approximately

Step-by-step explanation:

to find how much 20% of 15,998 does we multiply 15,998 with 20 and then divide it by 100

15,998 x 20 / 100 = 3,199

Subtract 8 1/5 - 4 2/5 . Simplify the answer and write as a mixed number.

Answers

Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]3\frac{4}{5}[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\8\frac{1}{5}-4 \frac{2}{5}\\-------------\\\text{Converting the mixed numbers into improper fractions...}\\\\\rightarrow 8\frac{1}{5} =\frac{41}{5}\\\\\rightarrow 4\frac{2}{5}=\frac{22}{5} \\-------------\\\frac{41}{5} -\frac{22}{5}\\\\\rightarrow\boxed{ \frac{19}{5}}\\-------------\\\\text{5 would go into 19 3 times with 4 as the remainder.}\\\\\frac{19}{5}=\boxed{3\frac{4}{5}}\\-------------\\\text{\textbf{Therefore:}}\\\\[/tex]

[tex]8\frac{1}{5}-4\frac{2}{5}=\boxed{3\frac{4}{5}}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

How to solve and what is the answer

Answers

Answer:

5

Step-by-step explanation:

Donald and Sara are surveying their neighbors about the community playground. Their questions, written on the survey, are below:

Donald: How many times do you visit the playground in a month?
Sara: Did you visit the playground this month?

Who wrote a statistical question and why?

Sara, because there will be variability in the responses collected
Donald, because every neighbor can give a different answer
Sara, because there can be only one answer to the question
Donald, because every neighbor will give the same answer

Answers

Answer:

B

Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too

i need help with these questions. anyone down to help me ?please

Answers

9514 1404 393

Answer:

A: less than 2 hoursB: 2 to 5 hoursC: more than 5 hours

Step-by-step explanation:

The attached graph shows the various company costs for x number of hours. The graph nearest the x-axis represents the lowest cost.

We can see that cost is lowest using Company A for 2 hours or less, and Company C for 5 hours or more. For times between those, Company B has the lowest charges.

Of course, the equation for charges in each case is the sum of the service fee and the product of hourly charge and number of hours (x).

__

I find the graphing calculator to be the most efficient tool for solving these. The alternative is to compare the equations pairwise to see which gives lower rates. With a little practice, you learn that the "break even hours" will be the difference in service fees divided by the difference in hourly cost.

For example A will cost the same as B when the $20 service fee and the $10/hour cost difference are the same: for 2 hours. A and C will cost the same when the $45 service fee and the $15/hour cost difference are the same, after 3 hours. B and C will cost the same when the $25 difference in service fees and the $5/hour cost difference are the same, after 5 hours.

So B is cheaper above 2 hours, and C is cheaper than that above 5 hours. With no service fee, A is cheaper for small numbers of hours (<2).

41:41
How many solutions does this linear system have?
y=-6x+2.
-12x - 2y = -4
O one solution: (0,0)
one solution: (1, -4)
O no solution
O infinite number of solutions
Answer is C

Answers

Answer:

Answer: B

Step-by-step explanation:

just solve keep up learning!

answer C
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what is the distance in the image below?

Answers

The distance is:

5 + 3 = 8 units

Since the segment is completely horizontal we need not to use formula for computing the length of a segment in 2D euclidean space.

Instead we can simplify the problem to a single dimension, only considering the x-coordinates of the endpoints of the segment.

The x-coordinates are -5 and 3.

Subtracting and applying absolute value yields the answer,

[tex]\mathrm{abs}(-5-3)=\boxed{8}[/tex].

Hope this helps.

Which are correct representations of the inequality -3(2x-5) <5(2 - x)? Select two options.

Answers

Answer:

-6x+15 < 10-5x

x>5

third equation, first graph

Step-by-step explanation:

Help please!!!!!!!!!!!

Answers

Answer:

y = 14

Step-by-step explanation:

[tex] \frac{15}{21} = \frac{5}{7} [/tex]

[tex] \frac{10}{x} = \frac{5}{7} [/tex]

[tex]x = 14[/tex]

Now,

10/15 = y/21

15y = 10*21

y = 210/15

y = 14

This is a Right answer...

I hope you understand..

Mark me as brainliest...

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