Answer:
2496144
Step-by-step explanation:
Total number of members of the senate on the finance committee (n)= 24
Number of members in each subcommittee(r) = 13
We need to make use of the combinations formula
C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]
1) Plugging in the values of n and r into formula, we get
C(24,13) = [tex]\frac{24!}{13!(24-13)!}[/tex]
= [tex]\frac{24!}{13!*11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14*13!}{13!*11!}[/tex]
2) Cancelling out the 13! from the top and bottom, we get
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11*10*9*8*7*6*5*4*3*2*1}[/tex]
3) Upon simplifying the numbers on the top and bottom, we get
C(24,13) = 2496144
46×.029 how can I show my steps
Answer:
For 46•.029
First you would show how you multiply 9 times six then 9 times 4 then you put it on the bottom
After that you would do 2 times six then 2 four then you put it one space down from the other aanswer and add them
Sorry ignore this if it’s complicated
Step-by-step explanation:
using a scale, or rate, of 1/4 inch per foot, calculate the rooms dimensions for your drawing
Answer: 81 in. (6.75 ft.) by 60 in. (5 ft.)
First, convert 27 ft. and 20 ft. to inches to make it easier to work with. This would convert like this:
27 ft. x 12 in. = 324 in.
20 ft. x 12 in. = 240 in.
This also means that the scale converts to 1/4 in. = 12 in.
Now, take your 324 in. and 240 in. and apply them to the scale.
For every 12 in. (1 ft.) in the non-scale room dimensions, there will be one 1/4 in. on the scale. That would apply like this:
324 in. (27 ft.) x
1/4 in. =81 in. [or 6.75 ft.]
240 in. (20 ft.) x
1/4 in. = 60 in. [or 5 ft.]
Step-by-step explanation: If incorrect sorry, Hope this helps!!
find the distance between the points (-3,-4) and (5,4)
find the distance between the points (-3,5) and (0,1 )
The distance between the points (-3,-4) and (5,4) is approximately 11.31 units, and the distance between the points (-3,5) and (0,1) is exactly 5 units.
To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean Theorem, which is
d² = (x2 - x1)² + (y2 - y1)²
Let's calculate the distances for the given pairs of points.
Distance between (-3,-4) and (5,4)
d² = (5 - (-3))² + (4 - (-4))²
d² = (8)² + (8)²
d = 64 + 64 = 128
d = √128
≈ 11.31
Distance between (-3,5) and (0,1)
d² = (0 - (-3))² + (1 - 5)²
d² = (3)² + (-4)²
d = 9 + 16 = 25
d = √25
d = 5
how much of the circle is shaded? Write your answer as a fraction in simplest form.
1/4 & 2/7
Based on the information given, it can be concluded that 35% of the circle is shaded, which is equivalent to the fraction 7/20.
What area of the circle is shaded?To understand what area of the circle is shaded, let's first calculate how much is not shaded:
First area: 1/4 = 0.25
Second area: 2/5 = 0.4
Total of the area that is not shaded: 0.65
The total area shaded: 1 -0.65 = 0.35
This means that the total shaded is 0.35. Now, let's convert 0.35 to a fraction:
[tex]\frac{35}{100} = \frac{7}{20}[/tex]
Based on this, the shaded area is 7/20
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-7(k-8)+2k
Please help. My mom doesnt think my answer is right :( my answer is 3k+(-1) and she thinks its -5k +56
Step-by-step explanation:
-7(k-8)+2k Use distributive property.
-7k+56+2k Combine like terms.
-5k+56
Mother knows best :)
HELP!! ANSWER IF YOU KNOW!!!
Solve:
7 = x + 12
A) -19
B) -5
C) 4
D) 5
Tom want to buy a sweater for $30.in which city will it be the most expensive
Answer:
Long Beach, California, tax = 10.25%
65 are drawing for a prize what is the probability for one person to win the prize
Answer:
1 in 65 chances.
Step-by-step explanation:
Please help me out with this problem
Answer:
1) Given
2) if lines are parallel, then corresponding angles are equal
3) Substitution
4) if altenate interior angles are equal, then the lines are parallel
6 + 5|2x -3| ≥ 4 pls pls pls help
Answer:
x is all real numbers
Step-by-step explanation:
6 + 5|2x -3| ≥ 4
The first step is to subtract 6 from each side
6 -6+ 5|2x -3| ≥ 4-6
5|2x -3| ≥ -2
Now divide each side by 5
5/5|2x -3| ≥ -2/5
|2x -3| ≥ -2/5
Absolute values are always positive. Our absolute value is greater than a negative number. It is always true. X can be any number and our absolute value will still be greater than -2/5.
x is all real numbers
Please HELP on geometry I need this answer quick. At a high school, the probability that a student is a senior is 0.20. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.05. What is the probability that a randomly selected student plays a sport, given that the student is a senior. A: 0.15 B: 0.05 C: 0.25 D: 0.33
Answer:
C: 0.25
Step-by-step explanation:
We will use conditional probability formula to solve our given problem.
[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,
[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.
[tex]P(\text{A and B})[/tex]= Probability of event A and event B.
[tex]P(A)[/tex]= Probability of event A.
Let us substitute our given values in conditional probability formula.
[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.
[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.
[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.
[tex]P(B|A)=\frac{0.05}{0.20}[/tex]
[tex]P(B|A)=\frac{1}{4}[/tex]
[tex]P(B|A)=0.25[/tex]
Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.
Answer:
probability that a randomly selected student plays a sport, given that the student is a senior is 0.25
Step-by-step explanation:
Let, A be an event that a student is senior.
Probability can be given as , p(A) = 0.20
B be the event where student plays a sport
Probability can be given as , p(B) = 0.15
We have given that the probability of a student is a senior and plays a sport is 0.05.
i.e p(A∩B) = 0.05
We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .
Use the formula: p(B/A) = p(A∩B) / p(A)
Plug corresponding values to get p(B/A).
p(B/A) = p(A∩B) / p(A) = 0.05 /0.20
p(B/A) = 0.25 , this is the answer
A line passes through the point (8,7) and has a slope of negative 3/4 Write an equation in slope-intercept form for this line.
The slope-intercept form for the line that passes through the point (8,7) and has a slope of -3/4 is y = -3/4x + 13. We found this by substituting the given slope and point into the slope-intercept equation and solving for b, the y-intercept.
Explanation:We're working on a mathematics problem here that involves the slope-intercept form of a line, which is usually written as y = mx + b. Here, m represents the slope of the line and b is the y-intercept, the point where the line intercepts the y-axis.
To write an equation for this line, we're given that the line passes through the point (8,7) and has a slope (rise over run) of negative 3/4, a negative value indicating the line decreases as it moves to the right.
We can substitute the slope and the given point into the slope-intercept equation to solve for the y-intercept: 7=(-3/4)*8+b, this simplifies to: 7=-6+b, and finally b=7+6 which gives us 13.
Therefore, the slope-intercept equation for this line with a slope of -3/4 and passing through the point (8,7) is y = -3/4x + 13.
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Final answer:
The equation of the line passing through the point (8,7) with a slope of negative 3/4 is y = -3/4x + 13 in slope-intercept form.
Explanation:
To write an equation for a line in slope-intercept form given a point and a slope, we use the formula y = mx + b, where m is the slope and b is the y-intercept. For a line that passes through the point (8,7) with a slope of negative 3/4, we first input the slope into the equation, getting y = -3/4x + b. We then substitute the x and y values from the point (8,7) into the equation and solve for b: 7 = -3/4(8) + b. This simplifies to 7 = -6 + b, and adding 6 to both sides gives us b = 13. Thus, the equation of the line in slope-intercept form is y = -3/4x + 13.
Evaluate the following.
Click on "Not a real number" if applicable.
Answer:
1) [tex]\sqrt{-64}[/tex] is not a real number.
2) [tex]-\sqrt{25} =-5[/tex]
Step-by-step explanation:
1) The square root of a number is defined for real numbers if and only if the number under the square root sign is greater than or equal to zero.
This implies that [tex]\sqrt{-64}[/tex] is not a real number because [tex]-64\:<\:0[/tex]
2) [tex]-\sqrt{25} =-\sqrt{5^2} =-5[/tex].
The number under the square root sign is [tex]25[/tex], which is greater than zero. Note that the negative sign is not inside the square root sign, it is outside it.
The value √-64 is not a real number, and -√25 is a real number.
√-64 and -√25 involve taking the square root of negative numbers, which results in complex numbers because real numbers do not have square roots of negative values.
Let's evaluate both:
√-64:
The square root of -64 is denoted as √(-64). In the realm of complex numbers, it's represented as 8i, where 'i' stands for the imaginary unit. So, √-64 = 8i.
-√25:
The square root of 25 is 5, and when you add a negative sign in front of it, you get -5. So, -√25 = -5.
In summary, √-64 is not a real number, and it is equal to 8i in the realm of complex numbers, while -√25 is a real number and equal to -5.
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Grant is planting one large tree and several smaller trees. He has a budget of $1400. A large tree coast $200. Each smaller tree is $150. How many total trees can grant purchase on his budget
He is buying one large tree, so subtract the cost of a large tree from the total:
1400 - 200 = 1200
He can spend 1200 on small trees.
Divide 1200 by the cost of a small tree to find how many small trees can be bought:
1200 / 150 = 8
He can buy 8 small trees.
Total number of trees = 8 small + 1 large = 9 total
What is the first step when solving the equation below for x 4x - 0.3 = 1.9
A. Add 1.9 to both sides of the equation
B. Subtract 0.3 from both sides of the equation
C. Divide each side of the equation by 4
D. Add 0.3 to both sides of the equation
Answer:
The answer my frind is D
Step-by-step explanation:
When you divide,
you must
blablabla
The first step in solving the equation 4x - 0.3 = 1.9 is to D) add 0.3 to both sides of equation, isolating the term with the variable 'x'.
Explanation:The question is asking how to begin solving the equation 4x - 0.3 = 1.9 for the variable x.
The first step in solving this equation would be to eliminate the subtraction part of the equation. In other words, we want to isolate the term with the variable, which is '4x' in this case. So our best course of action is to add 0.3 to both sides of the equation.This balances the equation and moves us closer to discovering what x is, so the correct option would be 'D. Add 0.3 to both sides of the equation'.
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What is the solution of this linear system? 2x + y = -4 y = -3x + 2
parentheses 3 squared - 2 cubed parentheses 66
[tex]( {3}^{2} - {2}^{3} ) ^{66} [/tex]
Answer:
1
Step-by-step explanation:
evaluate the parenthesis before raising to power 66
3² = 9 and 2³ = 8, hence
(3² - 2³)= (9 - 8) = 1
[tex](3^2-2^3)^{66}[/tex] = [tex]1^{66}[/tex] = 1
What is the measure of angles 5 and 6.
5
180°-(90°+68°)=180°-158°=22°
6
180°-22°=158°
Answer:
22° and 158°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles in the triangle from 180
∠5 = 180° - (90 + 68)° = 180° - 158° = 22°
∠5 and ∠ 6 form a straight angle, thus the angles are supplementary
∠6 = 180° - ∠5 = 180° - 22° = 158°
Hector went shopping for a computer. At RST store, a computer originally prices at $955 had a price reduction of 40%. What was the reduced price?
x 40
------ = --------
955 100
Cross multiply
955x40=38200
38200÷100=382
u get 382
955 -382= 573
$573
So here are the rules with change by percentage (m = percentage in decimal form, n = original, and r = new):
If increase: (1 + m)n = rIf decrease: (1 - m)n = rSince this is a price reduction, we will be following the second rule. In this case:
[tex]40\%=0.4\\\\(1-0.4)*955=r\\0.6*955=r\\573=r[/tex]
Answer:In short, the reduced price of the computer is $573.
Maria is in the state park riding her bike on the new bike trail. She starts at the beginning of the trail and rides for 4 miles. After the first 4 miles, her friend Aiden joins her and they ride the rest of the trail. By the end of the trail, Maria has been riding for two and half hours, while Aiden has been riding for two hours. Assuming they are both riding their bikes at a constant speed the entire time, how long is the bike trail?
Answer:
10 miles
Step-by-step explanation:
Thinking process:
The distance that Maria rides: 4 miles
Total time by Maria = 2.5 hrs
The friend = 2hrs
a weekly salary of $325 plus a 6.5% commission on sales at a store. How much would she make in a work week if she sold $4800 worth of merchandise?
Answer:
Income = 637
Step-by-step explanation:
Income = weekly salary + commission
commission = 6.5% * sales
commission = .065* 4800
= 312
Income = weekly salary + commission
Income = 325+312
Income = 637
*NEED MAJOR HELP!*
Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36.
A 2x + 14 = 36
B (2 • x) + (2 • 7) = 36
C 2x + 7 = 36
D 2(x + 7) = 72
E x + 14 = 36
F x + 7 = 18
Yes No Not Enough Information
Answer:
I believe a) is your answer
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(x+7)=36
Simplify: (Show steps)
2x+14=36
Pat listed all the multiples for 15. Write the numbers in pats list
Answer: Answer : Answer : 15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660,675,690,705,720,735,
Step-by-step explanation:
A snail moves 9feet in 3days at this rate how long will it take for the snail to move 15feet
1. In a certain company, 30 percent of the men and 20 percent of the women attend night school. If 40
percent of all employees are men, what percent of all the employees attend night school?
Answer: 24% of all employees attend night school.
Step-by-step explanation: If 40% of all employees are men and 30% of the men attend night school, we can multiply 0.40 by 0.30 to get the percentage of men who attend night school: 12% or 0.12. To find the number of women who attend night school, multiply 0.20 by 0.60(assuming percentage of men and women add up to 100%) to get 12%. Add 12% and 12% to get 24% of all employees attend night school.
x/ 2 = 7
A) x = 5
B) x = 7
C) x = 9
D) x = 14
Answer:
D) x = 14
Step-by-step explanation:
x/2 = 7
We want to isolate x
We can multiply by 2 on each side.
2 * x/2 = 7*2
x = 14
Answer:
14
Step-by-step explanation:
Well if you simplify or divide how ever you want to say it, it will be simplified to 7.
the intial value is also known as?
Answer:
Cauchy problem
Step-by-step explanation:
If you are talking about 'initial value problem', it is when talking about differential equations, an initial value problem is called a Cauchy problem by some authors as well. This is an ordinary differential equation together with a specified value which is called the initial condition. I really hope this helps!
The initial value is also known as the y intercept
What is the initial valueThe initial value, also known as the y-intercept or constant term, is a fundamental concept in mathematics, particularly in linear equations or functions. It represents the starting point or baseline on a graph, indicating the value of x is zero.
The y-intercept is where a line intersects the y-axis and serves as a reference for the function's behavior, influencing its direction and movement on the coordinate plane.
Hence we can say that The initial value is also known as the y intercept
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what is the area of a square with a diagonals of the length of 6?
Answer:
Area = 18
Step-by-step explanation:
We know that a square has side lengths of s
We can use the Pythagorean theorem to find s
a^2 + b^2 = c^2
We know that the hypotenuse or c = the length of the diagonal or 6
Substituting in what we know
s^2 + s^2 = 6^2
2s^2 = 36
Divide each side by 2
2s^2/2 = 36/2
s^2 = 18
Take the square root of each side
sqrt(s^2) = sqrt(18)
We only have to take the positive square root since it is a length
s = sqrt(9) sqrt(2)
s= 3sqrt(2)
The side length of the square is 3sqrt(2)
To find the area, we multiply the side by the side or s^2
s^2 = (3sqrt(2))^2
From above
s^2 = 18
Find the value of y when x = 4 in the equation 3x - 7/y = 1/3 Show your work help
Answer:
y = ⅗
Step-by-step explanation:
3x – 7/y = 1/3 Substitute the value of x
3×4 – 7/y = 1/3
12 – 7/y = 1/3 Multiply each side by 3
36 – 21/y = 1 Subtract 36 from each side
-21/y = -35 Multiply each side by y
-21 = -35y Divide each side by -35
y = 21/35 Divide numerator and denominator by 7
y = ⅗
=====
Check:
3×4 – 7/(⅗) = 1/3
12 -7×5/3 = 1/3
12 – 35/3 = 1/3
(36 – 35)/3 = 1/3
1/3 = 1/3
352 ft is ____ % of 2 mi; 2 mi is ____ % of 352 ft
Answer:
352 ft is 3.34% of mi ;
2 mi is 3000% of 352 ft
Step-by-step explanation:
To calculate : 352 ft is ___% of 2 mi and 2 mi is ___% of 352 ft.
We can calculate first:
352 is x% of 2 mi.
Solve for x;
Use conversion:
1 mi = 5280 ft
2 mi = 10560 ft
x% of 10560 ft means [tex]\frac{x}{100} \times 10560 = 105.60 x[/tex]
then, our equation become;
352 = 105.6 x
Divide both sides by 105.6 we get;
x = 3.333333...
or
x ≈3.34
Similarly, for
2 mi is y% of 352 ft
Solve for y;
2 mi = 10560 ft
y% of 352 = [tex]\frac{y}{100} \times 352 = 3.52y[/tex]
then;
10560 = 3.52 y
Divide both sides by 3.52 we get;
[tex]y = \frac{10560}{3.52}[/tex]
y = 3000
Therefore; 352 ft is 3.34% of mi ; 2 mi is 3000% of 352 ft