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

In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds.
a. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval.

Answers

Answer:

a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

b) [tex]T_c = 2.4469[/tex]

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469, and the answer to question b is [tex]T_c = 2.4469[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.

The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.

The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

what is sqrt 2x-3 = sqrt 3x-9

Answers

Answer:

x=6

Step-by-step explanation:

sqrt (2x-3) = sqrt (3x-9)

Square each side

(sqrt (2x-3))^2 = (sqrt (3x-9))^2

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

Check solution

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Solution is valid

sqrt (2x-3) = sqrt (3x-9)

Square each side

(sqrt (2x-3))^2 = (sqrt (3x-9))^2

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Therefore ans x = 6

Answered by Gauthmath must click thanks and mark brainliest

Use absolute value to express the distance between -12 and -15 on the number line


A: |-12-(-15)|= -37
B: |-12-(-15)|= -3
C: |-12-(-15)|= 3
D: |-12-(-15)|= 27​

Answers

C
I-12-(-15)l
l-12+15l
l3l = 3

in each figure below find m<1 and m < 2 if a||b

please help i don't have a lot of time I will give brainliest if you help

Answers

Answer:

m∠1 = 105°

m∠2 = 75°

Step-by-step explanation:

From the picture attached,

Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.

Therefore, m∠2 = 75° [Corresponding angles measure the same]

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 + 75° = 180°

m∠1 = 105°


In the figure above, AD and BE intersect at point C, and
the measures of angles B, D, and E are 98°, 81°, and 55°,
respectively. What is the measure, in degrees, of
angle A ? (Disregard the degree sign when gridding your
answer.)

Answers

answer in screenshot

Calculus II Question

Identify the function represented by the following power series.

[tex]\sum_{k = 0}^\infty (-1)^k \frac{x^{k + 2}}{4^k}[/tex]

Answers

With some rewriting, you get

[tex]\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k[/tex]

Recall that for |x| < 1, you have

[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]

So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to

[tex]\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}[/tex]

Based on known expressions from Taylor series, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex].

How to derive a function behind the approximated formula by Taylor series

Taylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.

In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:

[tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]

[tex]x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}[/tex]

[tex]x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)[/tex]

[tex]\frac{4\cdot x^{2}}{4+x}[/tex]

Based on power and series properties and most common Taylor series- derived formulas, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex] represents a Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex]. [tex]\blacksquare[/tex]

To learn more on Taylor series, we kindly invite to check this verified question: https://brainly.com/question/12800011

A box with a square base and no top is to be made from a square piece of carboard by cutting 4 in. squares from each corner and folding up the sides. The box is to hold 1444 in3. How big a piece of cardboard is needed

Answers

Answer:

[tex]C=27inch\ by\ 27inch[/tex]

Step-by-step explanation:

Squares [tex]h=4inch[/tex]

Volume [tex]v=1444in^3[/tex]

Generally the equation for Volume of box is mathematically given by

 [tex]V=l^2h[/tex]

 [tex]1444=l^2*4[/tex]

 [tex]l^2=361[/tex]

 [tex]l=19in[/tex]

Since

Length of cardboard is

 [tex]l_c=19+4+4[/tex]

 [tex]l_c=27in[/tex]

Therefore

Dimensions of the piece of cardboard is

[tex]C=27inch\ by\ 27inch[/tex]

Determine whether the statement below makes sense or does not make sense. Explain clearly. Based on our​ sample, the​ 95% confidence interval for the mean amount of television watched by adults in a nation is 1.9 to 3.5 hours per day.​ Therefore, there is​ 95% chance that the mean for all adults in the nation will fall somewhere in this range and a​ 5% chance that it will not.
A. The statement makes sense. There is​ 95% probability that the confidence interval limits actually contain the true value of the population​ mean, so the probability it does not fall in this range is ​100%−​95% =​5%.
B. The statement makes sense. There is​ 5% probability that the confidence interval limits do not contain the true value of the sample​ mean, so the probability it does not contain the true value of the population mean is also​ 5%.
C.The statement does not make sense. The probability the population mean is greater than the upper limit is​ 5% and the probability it is less than the lower limit is​ 5%, so the probability it does not is ​5%+​5%=​10%.
D. The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this.

Answers

The correct option is A because

The statement makes sense. There is​ 95% probability that the confidence interval limits actually contain the true value of the population​ mean, so the probability it does not fall in this range is ​100%−​95% =​5%.

From the question we are told that:

Confidence interval [tex]CI=95\%[/tex]

Mean [tex]\=x =1.9-3.5hours[/tex]

Level of significance (of the alternative hypothesis)

[tex]\alpha=100-95[/tex]

[tex]\alpha=5\%[/tex]

[tex]\alpha=0.05[/tex]

Generally

There is​ 95% probability that the confidence interval limits actually contain the true value of the population​ mean.

In conclusion

The  it does not fall in this range is Level of significance (of the alternative hypothesis)

​100%−​95% =​5%.

For more information on this visit

https://brainly.com/question/24131141?referrer=searchResults

I need answering ASAP please

Answers

Answer:

The choose (D) 1/3

I hope I helped you^_^

Solve for x

Answer options:
A) 6

B) 3

C) 5

D) 4

Answers

Answer:

it should be 3

Step-by-step explanation:

I hope this help

I'm interval notation please

Answers

9514 1404 393

Answer:

  (-2, 4]

Step-by-step explanation:

  -21 ≤ -6x +3 < 15 . . . . given

  -24 ≤ -6x < 12 . . . . . . subtract 3

  4 ≥ x > -2 . . . . . . . . . . divide by -6

In interval notation, the solution is (-2, 4].

__

Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.

Find the slope of the line containing the points (-3, 8) and (2, 4).

Answers

Answer:

-4/5

Step-by-step explanation:

The slope of the line is m=(4-8)/(2-(-3))=-4/5

The measure of angle tis 60 degrees.
What is the x-coordinate of the point where the
terminal side intersects the unit circle?
1
2
O
O
Isla Isla
2
DONE

Answers

Answer:

Step-by-step explanation:

Not a clear list of options and/or reference frame

Probably     0.5      if angle t is measured from the positive x axis.

A man starts repaying a loans with first insfallameny of rs.10 .If he increases the instalment by Rs 5 everything months, what amount will be paid by him in the 30the instalment.​

Answers

Answer:

30×5=150

so 150+10=160

thus his payment in the 30th installment is

rs.160

A ball thrown upwards hits a roof and returns back to the ground.

The upward movement is modeled by a function [tex]s=-t^2+3t+4[/tex]
s= −(t^2)+3t+4
and the downward movement is modeled by [tex]s=-t^2+3t+4[/tex]
s= −2(t^2)+t+7, where s is the distance (in metres) from the ground and t is the time in seconds.

Find the height of the roof from the ground.

Answers

Answer: 6 m

A ball thrown upwards from the altitude 4 m,

hits a roof and returns back to the ground.

upward movement:  s= −t²+3t+4

downward movement: s=-2t²+t+7

Step-by-step explanation:

Let's calculate the intersection:

[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]

Sorry, i have forgotten the picture.

You play a game where you roll a single die. You pay $1 to play, and the payouts are $0.50 if you roll an
even number, $2 if you roll a 1, and $1 if you roll a 3 or 5.
2. What are the odds for winning money if you play this game? Show your work and Explain.
dan
3. What is the expected value of this game? Show your work and Explain what the results mean.

Answers

All you do is first you ha

Triangles ABC and DEF are similar. Find the missing angles.

Answers

Angle A and D are similar
Angle B and E are similar
Angle C and F are similar

So this means they have congruent angles, meaning whichever angles are similar the angles will also be similar.

So since angle A is 62 degrees, angle D is 62 degrees too.

Since angle E is 80 degrees, angle B has to be 80 degrees as well.

All triangles add up to 180 degrees, so to find the angle measure of angle C and F, do:

180-(62+80)
180-142
= 38 degrees

So angles C and F are 38 degrees

Conclusion:
angles A and D: 62 degrees
angles B and E: 80 degrees
angles C and F: 38 degrees

*PLEASE HELP ME ILL GIVE BRAINLIST IF CORRECT*

Noah is playing a game where he must spin two wheels, each with 9 equal slices. There are 3 red slices, 3 green slices, 2 blue slices and 1 yellow slice on each wheel. If Noah spins and lands on a yellow slice on both wheels he wins, but if he lands on any other color, he loses. This information was used to create the following area model.


Is this a fair game? Why or why not?

A. Yes, the game is fair because Noah has equal probabilities of winning or losing.

B. Yes, the game is fair because Noah does not have equal probabilities of winning or losing.

C. No, the game is not fair because Noah has equal probabilities of winning or losing.

D. No, the game is not fair because Noah does not have equal probabilities of winning or losing.

Answers

Step-by-step explanation:

Yes, the game is fair because noah has equal probabilities of Winning

Answer:

No, the game is not fair because Noah does not have equal probabilities of winning or losing.

Step-by-step explanation:

which graph correctly represents this 2y+x=-5and y+3x=0

Answers

Answer:

you didn't feature any graphs for me to choose from

Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answers

Answer:

There is not enough evidence to support the claim that the bags are under filled.

Step-by-step explanation:

Given :

Population mean, μ = 433

Sample size, n = 26

xbar = 427

Variance, s² = 324 ; Standard deviation, s = √324 = 18

The hypothesis :

H0 : μ = 433

H0 : μ < 433

The test statistic :

(xbar - μ) ÷ (s/√(n))

(427 - 433) / (18 / √26)

-6 / 3.5300904

T = -1.70

The Pvalue :

df = 26-1 = 25 ; α = 0.05

Pvalue = 0.0508

Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled

Martin writes down 4
numbers.
Their mean is 8.
The range is 6.
The largest value is 11.
There is no mode.
Write down the four
numbers.

Answers

Answer:

5, 7, 9, 11

or

5, 6, 10, 11.

Step-by-step explanation:

The mean is 8 so the total value of the 4 numbers =  4*8 = 32.

Range is 6 so largest number - smallest = 6

The largest value is 11 so the smallest is 11-6 = 5

The middle 2 numbers add up to 32-(11+5) = 32 - 16

= 16.

- and as there is no mode they must be 7 and 9

or 6 and 10.

Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7) ​

Answers

Answer:

[tex]\displaystyle x \approx -4.28[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Natural logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 1 = ln(x + 7)[/tex]

Step 2: Solve for x

[Equality Property] e both sides:                                                                     [tex]\displaystyle e^1 = e^{ln(x + 7)}[/tex]Simplify:                                                                                                             [tex]\displaystyle x + 7 = e[/tex][Equality Property] Isolate x:                                                                            [tex]\displaystyle x = e - 7[/tex]Evaluate:                                                                                                            [tex]\displaystyle x = -4.28172[/tex]

e^1 = x+7

e - 7 = x

x = -4.28

Twice a number increased by the product of the number and fourteen results in forty eight

Answers

Answer:

Let x = the number. Then you have:

2x + 14x = 48 Collect like terms

16x = 48 Divide both sides by 16

x = 3

PLEASE MARK AS BRAINLIEST ANSWER

The number that satisfies the given statement is 3.

We are given that twice a number increased by the product of the number and 14 results in 48.

We will find the value of the number that we used in the given above statement.

Understand the meaning of the keywords used in the statement.

Increased means addition.

Product means multiplication.

Results mean equal to sign.

Let's write the given statement in equation form.

Consider P = the number

Twice a number = 2P

Increased =  +

Products of the number and 14 =  P x 14

Results in 48 = equals 48.

Combining all the above we get,

2P + P x 14 = 48

2P + 14P = 48

16P = 48

P = 48 / 16

P = 3

Thus the number that satisfies the given statement is 3.

Learn more about similar problems here:

https://brainly.com/question/17618748

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11. What is the midpoint of CD?
12. a. What are the exact lengths of
segments AB and CD?
b. How do the lengths of AB and CD
compare?
c. Is the following statement true or
false?
AB=CD

Answers

9514 1404 393

Answer:

  11. (-1.5, 3)

  12. √29, identical lengths, true they are congruent

Step-by-step explanation:

11. The midpoint is halfway between the end points. On a graph, you can count the grid squares between the ends of the segment and locate the point that is half that number from either end.

Points C and D differ by 2 in the y-direction, so the midpoint will be 1 unit vertically different from either C or D. That is, it will lie on the line y = 3. The segment CD intersects y=3 at x = -1.5, so the midpoint of CD is (-1.5, 3).

If you like, you can calculate the midpoint as the average of the end points:

  midpoint CD = (C +D)/2 = ((-4, 4) +(1, 2))/2 = (-3, 6)/2 = (-1.5, 3)

__

12. The exact length can be found using the Pythagorean theorem. The segment is the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

In the previous problem, we observed that the y-coordinates of C and D differed by 2. The x-coordinates differ by 5. Looking at segment AB, we see the same differences: x-coordinates differ by 5 and y-coordinates differ by 2. Then the lengths of each of these segments is ...

  AB = CD = √(2² +5²) = √29

a) The exact lengths of segments AB and CD are √29 units.

b) The lengths of the segments are identical

c) It is TRUE that the segments are congruent.

use quadratic formula to solve the following equation​

Answers

9514 1404 393

Answer:

  x = 2 or x = 9

Step-by-step explanation:

To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).

  2(3) +4(3(x -3)) = (x +4)(x -3)

  6 +12x -36 = x² +x -12

  x² -11x +18 = 0

Using the quadratic formula to find the solutions, we have ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]

The solutions are x=2 and x=9.

can some0ne help me?

Answers

Answer:

(x - 2)/3

(x - 4)/-5 or (-x + 4)/5

Step-by-step explanation:

this is an inverse function, and to solve an inverse function you would :

swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it

the first question's answer is :

g(x) = 3x + 2

x = 3(g(x)) + 2

x - 2 = 3(g(x))

(x - 2)/3 = g(x)

the second one is:

g(x) = 4 - 5x

x = 4 - 5(g(x))

x - 4 = -5(g(x))

(x-4)/-5 = g(x)

g(x) = 3x + 2

y = 3x + 2

x = 3y + 2

3y = x - 2

y = x/3 - 2/3

inverse g(x) = (x - 2) / 3

g(x) = 4 - 5x

y = 4 - 5x

x = 4 - 5y

5y = 4 - x

y = 4/5 - x/5

inverse g(x) = (4 - x) / 5

PLZ HELP QUESTION IN PICTURE

Answers

Answer: [tex]-\frac{9}{2}, -4, -3, -\frac{11}{4}, -2[/tex]

Step-by-step explanation:

slope = m

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-9}{-1-(-5)}=-4[/tex]

y = mx + b, (-5,9), (-1,-7), m = -4; (does not matter which point you plug in)

[tex]y=mx+b\\9=-4(-5)+b\\9=20+b\\b=-11\\y=-4x-11[/tex]

(now plug in each y value into the equation above)

[tex]7=-4x-11\\18=-4x\\x=-\frac{9}{2}\\\\5=-4x-11\\16=-4x\\x=-4\\\\1=-4x-11\\12=-4x\\x=-3\\\\0=-4x-11\\11=-4x\\x=-\frac{11}{4} \\\\-3=-4x-11\\8=-4x\\x=-2[/tex]

could someone please answer this? :) thank you

Answers

Answer:

The last one

Step-by-step explanation:

What we know:

We have a total of 16 coins

The 16 coins consist of dimes and quarters

The value of the coins is 3.10

The value of a dime is .10

The value of a quarter is .25

Using this information we can create a system of linear equations

First off we know that we have a total of 16 coins which consist of dimes and quarters

The number of Quarters can be represented by q and then number of dimes can be represented by d.

If we have a total of 16 coins then q + d must equal 16

So equation 1 is q + d = 16

Now we need to create a second equation

We know that the total value of the coins is 3.10 and we know that the coins consist of dimes and quarters

As you may know a quarter has a value of .25 cents and a dime has a value of 10 cents

If the total value of the coins is 3.10 the the number of dimes (d) times .10 + the number of Quarters times .25 must equal 3.10

This can also be written as

.25q + .10d = 3.10

So the two equations are

q + d = 16 and .25q + .10d = 3.10

These equations are shown in the last answer choice

Note: b is very similar to d

However the the value of the coins are incorrect in B

In B the value of the dime is represented by 10 which is not correct because the value of a dime is .10 not 10

A school has 4 different after school activities planned in the fall Janet has time to participate in 2 of these activities. How many different pairs of after-school activities can Janet choose from the available activities?​

Answers

Answer:

6

Step-by-step explanation:

Of 4 options, Janet has to choose 2. This is combinations as A and B is the same as B and A.

Combinations formula gives us 4!/ 2!2! , or 6.

please help me on this

Answers

Answer:

Median

Step-by-step explanation:

Using the median to measure central tendency, rather than the mean, is better for a skewed data set.

Since a skewed data set will have either very high or low extreme data points, the mean will be less representative and accurate when measuring central tendency.

Using the median will measure this better because it is not as vulnerable as the mean when there are extreme data points.

So, the answer is the median.

The answer is median his is because the mean value is depend on the correct media
Other Questions
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