Given:
Total number of members = 30
Number of democrats = 12
Number of republicans = 18
To find:
Number of different committees consisting of 8 democrats and 8 republicans are possible to be formed.
Solution:
Total number of ways to selecting 8 democrats from 12 democrats is
[tex]^{12}C_8=\dfrac{12!}{8!(12-8)!}[/tex]
[tex]^{12}C_8=\dfrac{12\times 11\times 10\times 9\times 8!}{8!4!}[/tex]
[tex]^{12}C_8=\dfrac{12\times 11\times 10\times 9}{4\times 3\times 2\times 1}[/tex]
[tex]^{12}C_8=495[/tex]
Total number of ways to selecting 8 republicans from 18 republicans is
[tex]^{18}C_8=\dfrac{18!}{8!(18-8)!}[/tex]
[tex]^{18}C_8=\dfrac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10!}{8!10!}[/tex]
[tex]^{18}C_8=\dfrac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}[/tex]
[tex]^{18}C_8=43758[/tex]
Now, number of different committees consisting of 8 democrats and 8 republicans are possible to be formed is
[tex]^{12}C_8\times ^{18}C_8=495\times 43758[/tex]
[tex]^{12}C_8\times ^{18}C_8=21660210[/tex]
Therefore, the total possible ways are 21660210.
Evaluate the function at the specified value and simplify
f(x)=|x|+8;f(-3)?
Step-by-step explanation:
f(x)=|x|+8
f(-3)=|-3|+8 =3+8 =11
bruh please, i beg...........................
Answer:
the answer is B
Step-by-step explanation:
Answer:
B, y = (x+2)^2+3
Step-by-step explanation:
Hi adenpetkowski, well to solve this problem we need to find the equation, so since a vertical parabola have equation of y = a(x-h)^(2)+k, where (h, k) is the vertex, we can use this formula to find the equation for the parabola, so since the vertex is (-2, 3) assuming it's lattice points, the formula now is y = a(x+2)^2+3, next, we can find a by taking a point from the parabola, say, (-1, 4). We then substitute the y and x to find that 4=a(1)^2+3, and we can find that a = 1. so the Formula is y=(x+2)^2+3. B
2. Evaluate the expression:
(5w^2+
+2) = (3p) for W= 4 and p = 3
At age 77, Eastman suffered from chronic pain due to a spinal condition. On March 14, 1932, after a reportedly jovial meeting with friends, he excused himself to write a brief letter before he 4535
The nth term of an AP is given by 2n +9 find the first term
Divide the number 90 into three parts in the ratio 1:4:5.
Answer:
9, 36, and 45
Step-by-step explanation:
The order is 9, 36, and 45 because as we have to divide 90 into 1:4:5, 1+4+5=10 total parts. Then 90 divided by 10 equals to 9. The first number has 1 part, so 9x1=9 for the first number. For 4 parts, 9x4=36 for the second number. For 5 parts, 9x5=45 for the third number. The order is 9, 36, and 45. Hope it helps!
When we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.
Given that,
The number is 90. We have to divide the above number in 1:4:5 ratio.
Based on the above information, the calculation is as follows:
x + 4x + 5x = 90
10x = 90
x = 9
Now multiply each ratio with 9 to get each value.
So, the values should be 9,36, and 45.
Therefore we can conclude that when we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.
Learn more: brainly.com/question/21416852
The equation 5y=6 represents purchasing 5 tubs of yogurt for $6 In this
equation, what does the solution represent?
Tell whether the sum is positive, negative, or zero without adding them.
-8 + 20
Answer:
The sum is positive.
Step-by-step explanation:
The 20 is a far greater value than -8, so no matter what, when you add them the sum will be positive. Though this would not be the same were the -8 greater than -20.
Hope this helps!
What are the answers to 11 and 12
Planes X and Y and points C, D, E, and F are shown.
Which statement is true about the points and planes?
С
VX
The line that can be drawn through points C and D is
contained in plane Y.
O The line that can be drawn through points D and E is
contained in plane Y.
O The only point that can lie in plane X is point F.
O The only points that can lie in plane Y are points D
and E.
E
.
Save and Exit
Next
Submit
Mark this and return
Answer:
The answer is below
Step-by-step explanation:
The planes are shown in the image below.
From the image, points D and E are on plane Y, while point F is on plane X.
A) The line that can be drawn through points C and D is contained in plane Y.
This statement is wrong because point C is not in plane Y
B) The line that can be drawn through points D and E is contained in plane Y.
Correct. Since both points D and E are on plane Y, hence The line that can be drawn through points D and E is contained in plane Y.
C) The only point that can lie in plane X is point F.
This statement is correct because from the image only point F is on plane X.
D) The only points that can lie in plane Y are points D and E.
This statement is correct because from the image only point D and E is on plane Y.
All of the following represent the same function except
All of the aforementioned represent the same function except: C. {(0, 1), (2, 3), (4, 5), (7, 8)}.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.
The types of function.In Mathematics, there are different types of function and these include the following;
Modulus functionSignum functionPeriodic functionInverse functionPiece-wise defined function.Logarithm functionFrom the first mapping, we can logically deduce the following:
when x = 1, y = 0
y = x - 1
0 = 1 - 1
when x = 3, y = 2
y = x - 1
2 = 3 - 1
when x = 5, y = 4
y = x - 1
4 = 5 - 1
when x = 8, y = 7
y = x - 1
7 = 8 - 1
For the ordered pair, we have:
when x = 0, y = 1
y = x + 1
1 = 0 + 1
when x = 2, y = 3
y = x + 1
3 = 2 + 1
when x = 4, y = 5
y = x + 1
5 = 4 + 1
Therefore, the function for these ordered pairs is equal to y = x + 1.
For the table of value, we have:
when x = 1, y = 0
y = x - 1
0 = 1 - 1
In this context, we can reasonably infer and logically deduce that all of the aforementioned represent the same function except {(0, 1), (2, 3), (4, 5), (7, 8)}.
Read more on functions here: https://brainly.com/question/20458982
#SPJ1
Alex needs to bisect ∠ABC using a compass and straightedge. He starts by performing the following steps. Step 1: Place the compass on vertex B of the angle. Step 2: Draw an arc that intersects both sides of the angle. Step 3: Label these intersections as point D and point E . Step 4: Place the compass at point D and draw an arc in the interior of the angle. What are the next steps Alex should take in his construction?
Answer:
Step 5: Without changing the length of the compass place it on point E and draw an arc in the interior of the angle.
Step 6: Draw a straight line with the straight edge that goes from the vertex and thru the intersection of both arcs.
Step-by-step explanation:
To bisect and angle is to split it prefectly in half, making for example a 90º angle into two 45º angles, in order to do this you will just need to use your compass and draw an arc that will pass over both sides of the angle, after that you put it in the intersections of the arc and the sides and just draw arcs that fit inside the angle from there where both arcs created from the intersections of the precious arc meet that's the middle of the angle, so now you just draw a straight line from the vertex to the intersection of both arcs and you just have bisected an angle.
A rickshaw company counted 39 ticket receipts last week. The price for a weekday ticket is $7, and the price for a weekend ticket is $9.50. The rickshaw driver collected a total of $333 for the week. Let x represent the number of weekend tickets and y represent the number of weekday tickets. Which system of equations represents the situation
Answer:
x+y = 39 and 14y+19=666
Step-by-step explanation:
Let x is the no of tickets for the weekend and y for the weekday.
The price for a weekday ticket is $7, and the price for a weekend ticket is $9.50. The rickshaw driver collected a total of $333 for the week.
Equation (1) should be :
x+y = 39 (because a rickshaw company counted 39 ticket receipts last week)
Equation (b) should be :
7y+9.5=333
Multiplying both sides by 2.
14y+19=666
Hence, the two equations that represent the situation are :
x+y = 39 and 14y+19=666
Answer: y = -x + 39
14y = -19x + 666
Step-by-step explanation:
There are two relationships given in the question. These are the number of tickets sold and the cost of the tickets sold. The total number of weekend and weekday ticket receipts is 39. This gives the equation x+y=39. Solving this equation for y gives y=−x+39. Now, we write an equation for the cost of the tickets sold. A weekday ticket costs $7, a weekend ticket costs $9.50, and the total money collected was $333. This gives the equation 7y+9.5x=333. Multiplying both sides by 2 to clear the decimal gives 14y+19x=666. This is equivalent to 14y=−19x+666.
Graph the solution of the inequality 2x - (3 – x) > x + 1 on the number line.
Answer:
do multiply
Step-by-step explanation:
and take line in right side
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.
The given inequality is 2x - (3 – x) > x + 1.
What is the solution of the inequality?A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement.
Now, 2x - (3 – x) > x + 1 can be solved as follows:
2x -3+x>x+1 (Simplify the bracket)
⇒3x-3>x+1
Subtract x on both the sides of the inequality.
That is, 3x-3-x>x+1-x
⇒2x-3>1
Add 3 on both the sides of the inequality.
That is, 2x>4
Divide 2 on both the sides of the inequality.
That is, 2x÷2>4÷2
⇒ x > 2
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.
To learn more about the solution of the inequality visit:
https://brainly.com/question/22010462.
#SPJ5
A company purchased mineral assets holding approximately 225,000 tons of ore for 855,000. The estimated residual value of the assets is zero. During the first year, 47,500 tons are extracted and sold. What is the amount of depletion for the first year?
Answer:
000.99
Step-by-step explanation:
complete the equation to fing the quotient of 2,275÷7
the quotient is that best of luck
What is the sum of 3x2+5x-6 and -x2+3x+9
Answer:
2x2+8x+3
Step-by-step explanation:
=3x2+5x+−6+−x2+3x+9
=(3x2+−x2)+(5x+3x)+(−6+9)
=2x2+8x+3
Each of the four shapes represents a positive whole number. The sum of the shapes in each row and column is displayed at the end of each row and column. Using this information, determine the numerical value of each shape.
Answer:
C₁ C₂ C₃ C₄ T
R₁ 4 3 3 1 11
R₂ 1 2 1 2 6
R₃ 2 3 4 2 11
R₄ 1 1 3 1 6
T 8 9 11 6
Step-by-step explanation:
1.-For inspection column 4 (C₄) is equal to row 2 ( R₂ ), and column 3 (C₃) is equal to row 1 (R₁)
2.- Let´s assume spiral is equal to 1 and the zebra rectangle is equal to 2
star 3 and pentagon 4
C₁ C₂ C₃ C₄ T
R₁ 4 3 3 1 11
R₂ 1 2 1 2 6
R₃ 2 3 4 2 11
R₄ 1 1 3 1 6
T 8 9 11 6
if 2 log x + 3 log y = 0, find y in terms of x.
Answer: If 2 log x + 3 log y = 0, find y in terms of x.
sorry for my messy handwriting!!!
Step-by-step explanation:
HELP! Giving branliest to who answers!!!
Answer: A. -1.8
Step-by-step explanation: Hi there!
First, we have to see the constant rate of change in the x and y values.
For x: 2
For y: -3.6
If the slope is m=y/x
then we can do
-3.6/2
that simplifies to
-1.8/1
which is
-1.8
Hope this answer helps you!
-73.3 as a mixed number
Answer:
- 73 3/10
Step-by-step explanation:
Step 1:
- 73.3 = -733%
Step 2:
- 733% = - 73 3/10
Answer:
- 73 3/10
Hope This Helps :)
9514 1404 393
Answer:
-73 3/10
Step-by-step explanation:
Pronouncing a decimal number can help when you convert it to a mixed number. This one is ...
"negative seventy-three and three tenths"
Of course, expressing "three tenths" as a fraction, you have 3/10.
Then your number is ...
-73.3 = -73 3/10
if f(x)= 4x+1 find f(3)
Answer:
13
Step-by-step explanation:
f(x)=4x+1
f(3)=?
f(3)= 4(3)+1= 12+1=13
Answer:
13
Step-by-step explanation:
x convert to 3
f(x)= 4(3)+1
f(x)= 12+1
f(x)= 13
I am not sure with the answer though, I just tried. I hope it helped you. ❤
Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true?
The percent error for this year was lower. Raul estimated better last year.
The percent error for this year was higher. Raul estimated better last year.
The percent error for this year was lower. Raul estimated better this year.
The percent error for this year was higher. Raul estimated better this year.
Answer:
3
Step-by-step explanation:
Answer:
C. The percent error for this year was lower. Raul estimated better this year.
Edge2021 <33 Please mark brainliest luv
How do you solve for x?
6th grade math I mark as brainliest
Answer:
1, 2, and 5
Step-by-step explanation:
Oxford, MS, has the highest elevation
Death Valley, CA, has the lowest elevation
The elevation of New Orleans, LA, is at sea level
I need help finding the function equasion of this table
X Y
0 0
1 4
2 16
3 36
4 64
QUESTION 17
Find the coordinates of the points that are 10 units away from the origin and have an x-coordinate equal to .6
Answer:
The set of all points that are 10 units from the origin is the circle centered at (0,0) with radius 10, which has equation
x2 + y2 = 100.
So, if the y-coordinate is -6, then x2 + 36 = 100.
x2 = 64
x = ±8
The points are (8,-6) and (-8,-6).
Find three consecutive even integers whose sum is -42
Answer:
Three consecutive even integers are x, x+2, x+4.
Step-by-step explanation:
Their sum is x+x+2+x+4 = 3x+6.
Hope this helped! <3
the cost for 25 square yards of carpet is $650. the cost for 40 square yards of carpet is $950
fun quashen answer this you will get 20 pointes it must be corret a clue it not B , D have fun be fast
Answer:
A. no, the sale price is about 60% of $65 or $39. Because $38 is less than $39, you do not have enough money.
Step-by-step explanation:
Given parameters:
Discount on sales = 40%
Amount with me = $38
Original sales price = $65.99
Unknown:
Will you have enough money to buy the item = ?
Solution:
To solve this problem, let us find the discount amount on the selling price;
= [tex]\frac{40}{100}[/tex] x 65.99
= $26.39
So, the price of the item now = Original sales price - discount amount
= $65.99 - $26.39
= $39.6
$39.6 can also be derived from 60% of $65.99
This amount is more than amount at hand.
Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In , the Amazon Alexa app was downloaded some 2800 times per day from the Google Play store (AppBrain website). Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2800 and standard deviation of 860. What is the probability there are 2000 or fewer downloads of Amazon Alexa in a day (to 4 decimals)? What is the probability there are between 1500 and 2500 downloads of Amazon Alexa in a day (to 4 decimals)? What is the probability there are more than 3000 downloads of Amazon Alexa in a day (to 4 decimals)? Assume that Google has designed its servers so there is probability 0.01 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle (to the nearest whole number)?
Step-by-step explanation:
What is the probability there are 2000 or fewer downloads of Amazon Alexa in a day (to 4 decimals)?
First, find the z-score.
z = (x − μ) / σ
z = (2000 − 2800) / 860
z = -0.930
Use a chart or calculator to find the probability.
P(Z < -0.930) = 0.1761
What is the probability there are between 1500 and 2500 downloads of Amazon Alexa in a day (to 4 decimals)?
Find both z-scores.
z = (x − μ) / σ
z₁ = (1500 − 2800) / 860
z₁ = -1.512
z₂ = (2500 − 2800) / 860
z₂ = -0.349
Use a chart or calculator to find the probability.
P(-1.512 < Z < -0.349) = P(Z < -0.349) − P(Z < -1.512)
P(-1.512 < Z < -0.349) = 0.3636 − 0.0653
P(-1.512 < Z < -0.349) = 0.2983
What is the probability there are more than 3000 downloads of Amazon Alexa in a day (to 4 decimals)?
Find the z-score.
z = (x − μ) / σ
z = (3000 − 2800) / 860
z = 0.233
Use a chart or calculator to find the probability.
P(Z > 0.233) = 1 − P(Z < 0.233)
P(Z > 0.233) = 1 − 0.5919
P(Z > 0.233) = 0.4081
Assume that Google has designed its servers so there is probability 0.01 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle (to the nearest whole number)?
Use a chart or calculator to find the z-score given the probability.
P(Z > z) = 0.01
P(Z < z) = 0.99
z = 2.3263
Now find the corresponding number for that z-score.
z = (x − μ) / σ
2.3263 = (x − 2800) / 860
x = 4801
Using the binomial probability principle, the probability values for the number of downloads are :
P(X ≤ 2000) = 0.1762 P(1500 ≤ X ≤ 2500) = 0.2981P(X > 3000) = 0.4081Maximum number of downloads = 4800Given the Parameters :
Mean, μ = 2800Standard deviation, σ = 860The Zscore formula ::
Zscore = (X - μ) / σ1.) Probability of 2000 or fewer downloads :
P(X ≤ 2000) = P(Z ≤ (2000 - 2800)/860)) = -0.930
Using a normal distribution table :
P(Z ≤ - 0.930) = 0.1762
2.) Probability of between 1500 and 2000 downloads :
P(1500 ≤ X ≤ 2500) = P(Z ≤ (2500 - 2800)/860) - P(Z ≤ (1500 - 2800)/860)
P(1500 ≤ X ≤ 2500) = P(Z ≤ - 0.349) - P(Z ≤ - 1.511)
P(1500 ≤ X ≤ 2500) = 0.3635 - 0.0654
P(1500 ≤ X ≤ 2500) = 0.2981
3.) Probability of more than 3000 downloads :
P(X > 3000) = P(Z > (3000 - 2800) / 860)) = 0.2325
P(Z > 0.2325) = 1 - P(Z < 0.2325)
Using a normal distribution table :
P(Z > 0.2325) = 1 - 0.5919 = 0.4081
4.) Number of downloads given a probability of 0.01
P(X > 0.01) ;
Using a normal distribution table :
The Z score corresponding to P(Z > 0.01) is 2.326
Using the Zscore formula to calculate the number of downloads, X ;
Zscore = (X - μ) / σ
2.326 = (X - 2800) / 860
2.326 × 860 = X - 2800
2000.36 = X - 2800
X = 2000.36 + 2800
X = 4800.36
Therefore, maximum daily download system is designed to handle 4800.
Learn more : https://brainly.com/question/12474772?