The probability of selecting five Democrats and two Republicans from the committee is approximately 0.3427.
To calculate the probability, we need to determine the number of ways we can choose five Democrats from eight and two Republicans from seven, and divide it by the total number of possible combinations.
The number of ways to choose five Democrats from eight is given by the combination formula C(8, 5), which is equal to 56. Similarly, the number of ways to choose two Republicans from seven is C(7, 2), which is equal to 21. The total number of possible combinations is C(15, 7), which is equal to 6435. Therefore, the probability is (56 * 21) / 6435 ≈ 0.3427, or approximately 34.27%.
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our class tutorial has 12 students, who are supposed to break up into 4 groups of 3 students each. Your Teaching Assistant (TA) has observed that the students waste too much time trying to form balanced groups, so he decided to pre-assign students to groups and email the group assignments to his students. (a) Your TA has a list of the 12 students in front of him, so he divides the list into consecutive groups of 3. For example, if the list is ABCDEFGHIJKL, the TA would define a sequence of four groups to be {A,B,C),{D, E, F},{G, H, 1}, {J, K, L}). This way of forming groups defines a mapping from a list of twelve students to a sequence of four groups. This is a k-to-1 mapping for what k? (b) A group assignment specifies which students are in the same group, but not any order in which the groups should be listed. If we map a sequence of 4 groups, ({A, B, C),{D, E, F),{G, H, 1},{J, K, L}), into a group assignment {{A, B,C),{D, E, F),{G, H, 1), (J, K, L}}, this mapping is ;-to-1 for what j? (c) How many group assignments are possible? (d) In how many ways can 3n students be broken up into n groups of 3?
(a) The mapping from a list of twelve students to a sequence of four groups is a k-to-1 mapping, where k is equal to 3.
Each group consists of 3 students, so when the list is divided into consecutive groups of 3, we have 4 groups in total. Therefore, each group assignment is determined by 3 students from the list, resulting in a 3-to-1 mapping.
The mapping is a 3-to-1 mapping because it assigns 3 students to each group.
(b) The mapping from a sequence of 4 groups to a group assignment is a 1-to-1 mapping.
In a group assignment, the order of the groups does not matter. As long as the students are assigned to the same groups, the assignment is considered the same. Therefore, the mapping is a 1-to-1 mapping, as there is only one possible group assignment for a given sequence of groups.
The mapping is a 1-to-1 mapping because each sequence of groups corresponds to a unique group assignment.
(c) The number of group assignments possible can be calculated by multiplying the number of ways to select 3 students from 12 for the first group, then the number of ways to select 3 students from the remaining 9 for the second group, and so on.
The number of ways to select 3 students from a group of 12 can be calculated using the combination formula "nCr," where n is the total number of students and r is the number of students to be selected. In this case, the formula becomes C(12, 3) for the first group, C(9, 3) for the second group, C(6, 3) for the third group, and C(3, 3) for the fourth group.
The total number of group assignments possible can be calculated as C(12, 3) * C(9, 3) * C(6, 3) * C(3, 3).
(d) The number of ways to break 3n students into n groups of 3 can be calculated using the multinomial coefficient formula.
The multinomial coefficient formula is used to calculate the number of ways to distribute objects into distinct groups, where the number of objects can vary in each group. In this case, we have 3n students to be distributed into n groups of 3, so the formula becomes (3n)! / (3!)^n.
The number of ways to break 3n students into n groups of 3 is (3n)! / (3!)^n.
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b) A cubical water tank has 1.5m as the length of its each side. Find the volume of the tank.
Answer:
3.375
Step-by-step explanation:
To get the volume of a cube you need to multiply length width and height since the cube is similar in length width and height you need to multiply 1.5 by itself three times.
V=l×w×h
V=1.5×1.5×1.5
V=3.375
Note:you need to multiply it to itself three times not to the number three.
Also it is only used if one number is given if three numbers are given multiply those three numbers hope this helps have a good day
A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B= A customer buys a drink.
What does P(A or B) = 0.45 mean in terms of this problem?
Answer:
b, the probability that a customer buys a taco, a drink, or both is 45%
P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
In terms of this problem, P(A or B) = 0.45 represents the probability that a customer buys either a taco (event A) or a drink (event B).
When we say "P(A or B)," it refers to the probability of either event A or event B occurring. In this case, it means the probability of a customer buying a taco or a drink from the food truck.
The value of 0.45 indicates the numerical probability associated with the event A or B. It represents the likelihood that a randomly selected customer from the food truck will purchase either a taco or a drink.
Therefore, P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
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TB
05-75 2/10,n/30 is interpreted as
The term "TB 05-75 2/10, n/30" represents the payment terms for a transaction.
The term "TB 05-75 2/10, n/30" provides specific information regarding the payment terms for a transaction. Here's a breakdown of its components:
1. "TB": This stands for "Trade Discount" and signifies that the terms are related to a discount offered for the transaction.
2. "05-75": The numbers indicate a cash discount percentage and a payment period. In this case, "05" represents a cash discount of 5%, and "75" indicates a payment period of 75 days.
3. "2/10, n/30": These terms further elaborate on the payment conditions. "2/10" means that a 2% cash discount can be taken if the payment is made within 10 days. The "n/30" portion implies that the net payment is due within 30 days from the date of the transaction.
In summary, "TB 05-75 2/10, n/30" signifies that a trade discount is offered, a cash discount of 5% is available if payment is made within 10 days, and the net payment is due within 30 days. It provides clear guidelines for the payment terms and discounts associated with the transaction.
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For the linear operator 2x х T := [ х y on R2, find the matrix representation B'[T]b relative to the ordered bases B' B s={1} -(0) [-1.0]
The matrix [T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] represents the linear operator T with respect to the bases B′ and B.
The matrix representation [tex][T]\left \{ {{B} \atop {B'} \right.[/tex] of the linear operator T relative to the ordered bases B' and B, we need to determine how the basis vectors of B' are transformed under the linear operator T and express them as linear combinations of the basis vectors of B.
B′={1} and B={(0),[−1.0]} we can represent the basis vectors as column matrices
[1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1]
[0][tex]\left \{ \atop {B'}} \right.[/tex] = [tex]\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]
[-1.0][tex]\left \{ \atop B' \right.[/tex] = [tex]\left[\begin{array}{ccc}-1\\0\\\end{array}\right][/tex]
Now, we can apply the linear operator T to the basis vectors of B' and express the results in terms of the basis vectors of B.
T([1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1] = 1.[0][tex]\left \{ \atop {B'}} \right.[/tex] + 0.[-1.0][tex]\left \{ \atop B' \right.[/tex]
Therefore, we have
[T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex]
The matrix [T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] represents the linear operator T with respect to the bases B′ and B.
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Solve for x and then answer
Answer:
Value of x = 70'
Step-by-step explanation:
Given:
Given quadrilateral is a cyclic quadrilateral, in a cyclic quadrilateral sum of opposite angle is 180' .
Find:
Value of x
Computation:
x' + 110' = 180'
x' = 180' - 110'
Value of x = 70'
please help thank u alot going to put pictures!
PLz help
how would you represent this situation( Write the equation or inequality.)
On a carnival ride you must be at least 42 inches tall to ride
Answer:
x≥k y for you y≥42 inches tall
Step-by-step explanation:
can i have brainliest if right
a string runs up and to the left in the x-y plane, making an angle of 29◦ to the vertical. determine each component of the unit vector that points along the string, beginning with ˆrx.
To determine the components of the unit vector that points along the string, we need to break down the vector into its x and y components.
Given that the string makes an angle of 29 degrees to the vertical, we can define the unit vector as follows:
ˆr = ˆrx + ˆry
To find the x-component (ˆrx) of the unit vector, we can use the cosine of the angle:
cos(29°) = ˆrx
To find the y-component (ˆry) of the unit vector, we can use the sine of the angle:
sin(29°) = ˆry
Let's calculate the values:
ˆrx = cos(29°)
ˆry = sin(29°)
Using a calculator or mathematical software, we can find the numerical values of ˆrx and ˆry:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
Therefore, the components of the unit vector that points along the string are approximately:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
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20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
Answer:
2.88 mi
Step-by-step explanation:
The equations y = 5x and y = –1∕5x + 4 represent what types of lines?
Answer:
It might be perpendicular lines
Step-by-step explanation:
What is the sum of 2 with exponent of 4 and 7 with an exponent of 2. please write in standard form.
Answer:
I think the answer would be 65 , because :
2^4 + 7^2 = 16 + 49 = 65 .
hope it helps u ^.^
Answer:
65
Step-by-step explanation:
First you would solve the exponent and then you would add them
2 to the power of 4 = 16
7 to the power of 2 = 49
16 + 49 = 65
2 to the power of 4 + 7 to the power of 2 = 65
Purple paint is made of a ratio of
16 white : 3 blue : 1 red
how much white paint is needed to make one gallon of purple paint?
plz help its important
there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint (got it from safari)
(450) + (28.75x) = 967.50
solve for x
Answer:
x=18
Step-by-step explanation:
Answer:
x= 18
Step-by-step explanation:
To solve this equation you have to work backwards
Start by dealing with the numbers that we know:
450 + (28.75 × x) = 967.5
-450 -450
28.75x = 967.5
(when a number and a letter in mathematics are next to each other they are multiplying)
Now divide to find the value of x:
967.5 ÷ 28.75 = 18
18 is the value of x
how many 5-digit passwords can I make out of the English alphabet. lowercase only
Answer:
7,893,600 different combinations
Step-by-step explanation:
Answer:
We have a total.of 26 alphabets in the english language and numbers 0 to 9 will be 10.
Since there are no other limitations, we have to arrange 8 places with the 36 options we have.
It will simply be 36c8.
The answer will be 3,02,60,340.
Use the following picture to find the measure of angles 3 and 4. (picture)
Jackson has a table with a square top and he wants to buy a circular piece of lace
that will cover the entire top of the table. The top of the table has side lengths of 12
inches, as shown.
12 in
12 in
What is the area, in square inches, of the smallest circular piece of lace Jackson could
Answer:
144
Step-by-step explanation:
the area is 144 im prob wrong
If ab=8 and a^2+b^2=16 then what is the valué of (a+b)^2 PLSS HELP NOW
I think that i got it but at the same time not sure but the value of a+b should be 14+20
At a constant speed, a car travels 75 miles in 60 minutes. How far does
the car travel in 18 minutes? If you get stuck, consider using the table.
Answer:
22.5 miles
Step-by-step explanation:
75/60 = x/18
60x = 1350
x = 22.5
100 - x2 + 15, cuando x = 9
Sasha had to run 1/3 of a mile. She decided to walk, jog, and run the 1/3 mile, in equal parts. What fraction of the mile will she run?
A.9
B.3/9
C.1/9
D.3/3
(Need help asap pls)
Answer:
C 1/9
Step-by-step explanation:
She needs to run 1/3 of a mile and is going to run/jog/walk that 1/3 mile
So she must do 1/9 of a mile running, 1/9 walking, and 1/9 jogging because 1/3 is equivalent to 3/9.
Since she is going to run/jog/walk the same amount of the 1/3 she is going to run 1/9 of the 1/3
Let me know if I'm wrong
Hope I helped :]
Use the spinner below for each of the following
questions. Place an "x" along the number line to
represent how likely the event is to occur.
How likely is it for the spinner to land on a 5?
A random sample of n_1 = 555 individuals results in x_1 = 451 successes. An independent sample of n_2 = 600 individuals results in x_2 = 510 successes. Does this represent sufficient evidence to conclude that p_1≠ p_2 at the α = 0.05 level of significance?
There is no sufficient evidence to conclude that p₁ ≠ p₂
How to determine if the conclusion is sufficientFrom the question, we have the following parameters that can be used in our computation:
n₁ = 555
x₁ = 451
n₂ = 600
x₂ = 510
Calculate the pooled sample proportion using
p = sum of x/sum of n
So, we have
p = (451 + 510)/(555 + 600)
p = 0.832
Calculate the test statistic using
[tex]z = (\frac{x_1}{n_1} - \frac{x_2}{n_2}) \div (\sqrt{(p * (1 - p) / n_1) + (p * (1 - p) / n_2)}}[/tex]
So, we have
[tex]z = (\frac{451}{555} - \frac{510}{600}) \div (\sqrt{(0.832 * (1 - 0.832) / 555) + (0.832 * (1 - 0.832) / 600)}})[/tex]
When solved, we have
z = -1.699
The critical value at α = 0.05 level of significance is 1.645
The z = -1.699 is less than this value
This means that we fail to reject the null hypothesis
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how do i solve 60=2b+20 also show me how u did ur work please
Answer: b=20
Step-by-step explanation:
First for the equation 60=2b+20
We will subtract 20 from both sides to start isolating b
40=2b
Divide both sides by 2
and you get b=20
Answer:
b = 20
Hope This Helps!
Step-by-step explanation:
60 = 2b + 20
-20 -20
--------------------
40 = 2b
40/2 = 2b/2
20 = b
b = 20
A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, round to the nearest tenth?
Answer: 2035.8
Step-by-step explanation:
The volume of the cylinder is 2034.72 cubic ft
What is the volume of the cylinder?The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold or we can say the volume of a cylinder is the number of unit cubes that can be fit into it. The formula for volume of cylinder is V = A × h
Assuming the given cylinder is Right Circular Cylinder
Then the formula is V = πr²h
From the question radius (r)= 6ft
height (h)=18ft
volume (V)= π× 6² × 18
=2034.72 cubic ft
Thus the volume of the cylinder is 2034.72 cubic ft
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What is the slope of the line that
passes through these two points?
(1, 2)
(2, 8)
(x1.yı) Slope =
rise (y2-yı)
Remember, given two points,
(x2:y2) run (x2-x1)
Answer:
6
Step-by-step explanation:
8 - 2 / 2 - 1
6 / 1
6
Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by
T(x) = 7-9(x-2)2-3(x-2)3
a. find f(2) and f '' (2).
b. Is there enough information given to determine wheather fhas a critical point at x = 2?
If not, explain why not.
If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.
c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?
If not, explain why not.
If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.
d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.
Solution :
Given : [tex]$T(x)=7-9(x-2)^2-3(x-2)^3$[/tex]
a). f(2) = T(2) = 7
[tex]$\frac{f""(2)}{2!} =-9$[/tex] , so f''(2) = [tex]$-18$[/tex]
b). Yes, since f'(2) = T'(2) [tex]$=$[/tex] 0, [tex]$f$[/tex] does have the critical point at [tex]$x=2.$[/tex]
Since f''(2) = [tex]$-18$[/tex] < 0, [tex]$f(2)$[/tex] is relative maximum value.
c). [tex]$f(0)=T(0)=-5$[/tex]
It is also not possible for determining if [tex]$f$[/tex] has a critical point at x = 0 because [tex]$T(x)$[/tex] gives exact information only at [tex]$x=2.$[/tex]
d). The Lagrange [tex]$\text{error}$[/tex] bound [tex]$=\frac{6}{4!}|0-2|^4= 4$[/tex]
[tex]$f(0) \leq T(0)+4 = -1$[/tex]
Therefore, [tex]$f(0)$[/tex] is negative.
please answer ASAP AFAP PLEASE PLEASE ANSWER RIGHT OR I'LL REPORT YOU TO BRAINLY . but on the other hand if you answer correctly I'll just give you brainliest, and go to your profile and thank you and give you a 5 star rating!
Answer:
The answer is B. 4.4 oz.
Step-by-step explanation:
What do we know? We have the 6-pack of 12-ounce bottles and they cost $2.99, we also know that the other bottle 67.6 ounces that also costs $2.99.
Forgot the money, we're just going to be looking at the ounces.
First, we take the 6-pack and multiply by 12 because we want the size as one, rather than seperate. 6 x 12 = 72
The question is asking how many more ounces are you getting if you purchase the 6-pack. In order to do this, we take the 72 ounces that we got and subtract that 67.6 ounces of the other drink. 72 - 67.6 = 4.4
The ounces saved are 4.4 ounces.
G(x)= x^2 + 5x
g(-3)=
Answer: The answer is g=x/16
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
g(-3) = (-3)^2 + 5(-3) [Take x value as -3]
= 9 -15
= -6
Sarah donated $920 for a new park. Sarah's brother donated $850. How much more money did Sarah donate?